If you open the account you will have to pay, that's just the deal. 

You should be logging work in the correct category, which often transcends type of work, unless it's something really specific. Redlines could be half the categories. What phase of design are these projects in? That will probably tell you right where you should put them. 

You should go ahead and pay the NCARB fee and record your AXP hours as you complete them.  It will be cheaper and easier on you in the long run.   I believe NCARB now penalizes people that don't report hours within 6 months of accruing them.

Your goal should be to get the needed AXP hours as fast as you can and take the exam.  You are doing well by starting while you are still in school.

It's great to get those hours logged as soon as possible and worth the initial and yearly fees. Make sure to check your state's rules as they often have different requirements with some requiring x years experience post school. This doesn't mean you should put off AXP - get any hours you can as some categories are harder to fill than others. Too many never start the process and wind up with kids etc and just never get around to getting the license as the school test taking mindset has long worn off. Some employers in the future - post school - may even ask if you've started the process as a sign of initiative. 9/10 the work you're describing will fall under construction documentation (or some variant of that wordage). I believe you need the most of these hours.