Training for the 800 to improve 1600m

You won't "ruin" your base by competing in the 800. As long as you continue your base-type training (LT runs, hill reps, long runs, relaxed distance) you'll continue to build your endurance during indoor season. And keep up the regular speed development and strength training days, as those should help improve your basic speed without the risk of eroding your aerobic foundation. On the speed stuff, gradually lengthen some the reps over the winter, building up to some 100-150 meter reps @ 400 goal pace with long recoveries to improve your speed endurance.

And yes, improving your 800 can improve your 1600-3200 performance, as long as you keep working to improve your aerobic foundation. It sounds like you are a "distance" type (rather than a 400-800 type), so your base training for all of your competitive track distances (800-3200) should be pretty much the same.

One more thing. Since you'll be racing a lot during the indoor season, be sure to focus on recovery on the day(s) after meets with easy aerobic runs until you feel pretty well recovered.

Run them all! Not all in the same meet of course. If you have two meets in a week half one where you go shorter like the 4x8, 800,400, distance 4x2 or some combo of that and maybe the 2mi the second. I generally would have my athletes rotate what they race each week based on their goals. We raced a little less than that as well and no two meets in a week.

63 for 400 is rookie numbers. Regardless of male or female or what distance, you need to improve your speed, so yes, get after it!

Unless you're a 4/8 type of guy, your training should prepare you for both at this stage of training. You shouldn't be specializing too heavily by doing very specific workouts until spring, you should be mixing it up by doing mile pace work and 800 pace work biweekly or and/or multi-pace workouts. You can choose to race whatever you'd like or where ever your coach puts you.