Just going to throw my hat in there to answer some of your questions from my perspective. It might just be supplemental to Killey, but I play K' a bit more defensive so I make a lot of use out of his normals.
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Question 1 (Sweep): Killey already mentioned the main portions, but you can use his sweep as a hit confirm into a combo. You can cancel the sweep into EX Chain Drive which is an anywhere juggle. If you condition people to stand block, either through tick throwing or mixing up your ground pressure with hops, it will net you a decent 40% at max for two bars alone.
Since K' isn't a combo heavy character or mix-up heavy character, you have to make use of his normals to trick or pressure people.
Question 2 (Hop Pressure Strings): Again, Killey covered a lot of this, but I have something to say. j.D is a very good normal when used properly. The arc and range of j.D is one of the most horizontal reaching normal K' has. He can hop at someone and tag them a full character length with his hop D. It's also a decent air-to-air which you can buffer qcb+K in the air to net extra damage in exchanges.
Part of hop pressure strings is also poking. You're not always going to move forward. By timing hop D, you can hit people from farther away and poke them with cr.B once at max range. This keeps you relatively safe because you don't have to commit to getting in someone's space. You can use this to hop forward from a distance and keep applying pressure from a safe position. You can use this by jumping straight up after jumping on someone with another normal or j.CD. You can step away from them a little out of their throw range and tag them with a j.D from really far away. This works wonders in the corner where jumping straight up presents a wall they can't cross. j.CD, j.B, and j.D can pressure people heavily even when you're just hopping straight up as it keeps them from advancing forward.
Some pieces of hop pressure is trying to condition people into a cross up situation. For K', his usual cross up options are j.A and j.C, but now with our discovery above, you can setup to even have j.D cross up. Cross ups are mostly ground based so we'll ignore that for now.
Question 3 (Corner Pressure Strings): Again, gonna just add on to Killey's comments. K' does not have particularly safe specials. Ein trigger follow-ups are unsafe and even Ein Trigger is fairly slow with considerable recovery. That being said, you don't always want to rely on this. Corner pressure is also about keeping people in the corner in a state of panic. K' has a fairly long reaching cr.B and st.A. Without pushback, you can mix in gaps for people to react to or not react to. For example, you can tick away with cr.B once and do st.A to check a hop. If they duck, it whiffs, but the recovery is very fast on whiff. If they tried to jump, you put them in an air reset. Reacting to these situations where there's a fork is also important. Using this example, if they ducked, they're not in a position to tech a throw. Also because you whiffed a normal, they're not in block stun. You can proceed to attempt a tick throw. If they air reset, you can throw out a meaty (+6) regular ein trigger which will put them in a frame trap. You could throw out another normal to poke them.
You can also give them space after knock downs. Get just outside of their jump range and poke them with d.B into Ein Trigger. Even if it whiffs, if they make a motion to move forward, they'll get tagged by the Ein Trigger. Using A Ein Trigger knocks them down while C keeps them standing. I alternate, but using A in the corner gives you more air reset options so liberally use A Ein Trigger.
Poking people from a safe distance also encourages them to jump. Using vertical jumps to present a wall is also a form of pressure and attrition in the corner. K' can make use of this with early j.CDs, j.Bs, and j.Ds. They're very good, you can confirm off of them into HD, and two of them are air cancel-able so you can do qcb+K for extra damage.
In the corner, you can use strings like cr.B x3 and cr.B, cr.A, cr.B because they're pinned up against the corner. Delay them as any hit can turn into a hit confirm. You can also tag people a lot with st.B from afar because it's a mid-body normal that hits crouching and standing opponents. Use it to poke after strings to check people who might be jumping or pressing buttons. Also, part of strings is taking your foot of the gas. You can back dash or roll backwards to bait out reversals or throw off a counter-poke so you can open them up when they whiff.
Frame traps like cr.A (delay) cr.B or cr.B, st.C are great in the corner because they continue your ability to leave small gaps people react to. Use this more so when people are trying to press buttons to poke you rather than when they roll.
If they're in the corner and they roll, use your frame traps and walk back and forth a little. Don't feel like you have to commit. You can catch roll outs a lot easier if you give them some space or are not committing to a block string.
Question 4 (Ground Pressure Strings): So now we're in mid-screen, this gets a bit more difficult. K' can't get very good damage off of poking because after one or two normals, he can't get no-meter carry combos. You should stick to confusing people with frame traps I mentioned earlier, cross ups I mentioned earlier, and light block strings into running.
You can do a lot to confuse people without jumping. However, in mid-screen that's really going to use a lot of meter. His EX Black out, after 2 cr.Bs will cross people up on the other side. You can use that (sparingly) to get around people and throw off their thoughts. You can confirm with EX Ein Trigger into a combo. If you connect with two cr.Bs only, f+B follow up is better. If you got a confirm off your hop pressure, be safe and just do f+D. Either one is fairly safe.
Other than that, if you want to stick in on people, mixing in running in to low normals or running in for a tick throw is a 50-50 mix up from one or two cr.Bs. You could also delay a C Ein Trigger and use the f+B follow up to tag people pressing buttons. Using C Ein Trigger in midscreen is better because on hit, you can connect f+B for extra damage. Although they're standing, soft knockdowns are not as useful all the time because people can tech. C Ein Trigger on hit is, in my opinion, 0 frames of advantage. It also puts you in a position to react to what they do in response on block or hit.
A risky mid-screen tactic is to pressure people and hit them with Minute Spike as a whiff punisher. You're not using it to continue pressure, but you can use it to encourage people not to whiff normals after your blockstrings which will allow you to bring in elements like running forward for tick throws (or walk, it's safer).
This same tactic can be used if you learn how to bypass Minute spike to Narrow spike for a low. At max range, B narrow spike is -5 and hard to punish because of the distance. The EX version is -3 point blank and relatively safe at a max range so you can use this to continue pressure or get in. Just be wary of grapplers like Daimon and Raiden as they have far reaching grabs.
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Well, those are my tactics. They're pretty basic. Just wanted to add a few elements to Killey's advice.
