El Chaltén

Your El Chalten instinct is *perfect* for (1). Mid-February is prime Patagonian summer - long daylight hours, best hiking weather. 5 days is solid for the big hikes: - Laguna de los Tres (Fitz Roy viewpoint) - the iconic one, do it on your clearest weather day - Laguna Torre - equally stunning, less crowded - Loma del Pliegue Tómbado - underrated panoramic views of both peaks. El Chalten is basically built for solo female hikers. It's a tiny backpacker town (no cars needed), everyone's there to hike, and the trails are well-marked. Very safe. Budget-wise you'll be fine at $100/day - hostels are cheap and you'll mostly pack your own trail lunches.

This time why don't you spend only a few days in TDP and then go over to the Argentina side and do El Chalten and el calafate. El Chalten is much easier to do (doesn't require all the planning of TDP/W Treks)

You can use more time going to El Chalten after Calafate.

We did 2 nights in El Chalten and hiked the "Laguna de los tres" hike, which is the hardest thing I have ever done in my life LOL. (But really worth it!!!)

then grab a rental car and head straight to El Chalten, spent at least 3 nights there and enjoy any of the great trails up there(Laguna Los Tres).