I use s slightly different method for the DG (and winged vessels like it such as the DGIV) that is a bit more efficient. It's closer to the ascent profile used by the XR series vessels, but without the scram engines, of course.
The profile given in the checklist is based on the theory that you want to reduce aerodynamic drag as much as possible during the entire ascent, but this means using thrust to overcome gravity quite a bit. You've noticed that the velocity indicator drops below 5 degrees (indicating a high AoA) most of the ascent.This means that more of your thrust vector is in a "upward" direction instead of a forward direction - and forward (tangential) velocity is what you need to attain orbit. Also, the higher AoA increases the drag coefficient quite a bit, so it can often be better to be a little lower. Even though you are in a denser part of the atmosphere, the lower drag coefficient results in LESS velocity lost to drag.
I basically break down the ascent into different stages.
1: Launch. At very low altitudes drag is very high, so get into the air and reduce throttle to maintain speed, about 200 m/s. and turn to the desired heading. Once the heading is attained, go full throttle and pitch up to about 75 - 80 degrees. Watch the ACC on SurfaceMFD, and use pitch to attain a slight ACC of a couple m/s. One you've done this leave the stick alone for the rest of the ascent - use elevator trim only (Insert and Delete keys, IIRC)
2: Transition. Once you are at least 8k to 10k alt (and should still be subsonic - 250m/s max) use downward elevator trim to begin lowering the nose. The stock DG's trim is a it "weak". so use full downward trim. A DGIV's is a bit stronger, about -.8 is better. The goal is to get near level flight around 25K alt. Watch the VS, target is about 200 m/s at this stage.
3: Acceleration: Use elevator trim to gradually reduce VS, about 150m/s at 30k, as sow as 100 m/s by 35k. If the nose drops even with full up trim just let it. As you gain speed it will come back up. By thi time you get to 70k you want a velocity of over 7km/s, and your ApA should be climbing rapidly.
4: MECO: Aoround 70k to 75k you should be near 7.5kms, and your ApA should have risen to around 200k. Cut the main engines and coast. Watch the ApA, if it's rising apply a bit of downward trim, if it's lowering trim up. Ussually a couple clicks of down trim will keep the ApA stable. Once over 125k you can engage prograde AP and some time accel.
5: Circularize. Once you get to your Apo, use main engines to raise the PeA and circularize the orbit.
Note that RCS wasn't used until the prograde Ap was engaged- in fact it's hand off the stick entirely after the intial pitch up manuever.
As for your second question, 50k is close enough for an initial rendezvous if your relative velocity is low ( under 300m/s). You should be using DockMFD and have the COM/NAV 1 set to the ISS's transponder (not an individual port freq), and ensure the docking hud is active and set by pressing the <HUD> key once DockMFD shows it's getting a signal. Pay attention to the RVel when you stop getting closer - if it's over a couple hundred m/s, it likely means your planes have gotten out of alignment - fix that then try again. The DG has tons of thrust, so if your RVel is under 500 m/s you can usually still succeed. One you stop closing on the ISS, turn toward the negative RVel indicator (the plus sign, will be 180 degrees from the "plus sign in a ball". Use main engines to reduce the RVel as much as possible, 1 or 2 m/s max. Then point at the ISS and give a bit of thrust to get about 20 m/s RVel. Use lienear RCS to keep the plus sign near the RCS as you close. Use bursts of time accel - don't increase RVel. Then you can pick a port and dock.
IMFD has a program (under the Orbital Ops menu) to null relative velocity, this can be handy as it's very difficult to do this manually - once RVel gets below 5 m/s the vector will start moving quite a bit.
BTW, welcome to the forum, and congratulations on getting that close without help! The main secrets to rendezvous and docking are patience and precision. Keep the planes aligned within a couple hundreths of a degree, and keep the RVel low.