I think 5:2 could be used easily enough for recomposition. To adapt it, I would aim to eat about 300 calories over maintenance on your normal days, and eat a little less on fasting days. Basically the excess on normal days will be used to build some muscle tone, and the fasting days will then effectively serve to shave off any residual fat.

The one thing you will want to be mindful of is the overall weekly deficit, as whatever that is will decide your overall weight. In your case I imagine you don't want to lose much more, so you would want a small enough weekly deficit at best.

If you're considering alternatives, Leangains is a very good protocol for recomposition also. You should be able to adapt 5:2 easily enough for recomp, but Leangains is already designed for it, so you wouldn't have to adapt anything.

Re: resistance training, you're right, that is the critical component. Basically it is the stimulus to your muscles to grow. You don't need weights though, unless you're set on using weights that is. I use a great bodyweight programme from startbodyweight.com, and much prefer remaining gym-free personally, as well as reaping some of the other benefits that bodyweight training offers such as improvements in balance, co-ordination, and the strengthening of joints and soft tissues.

Bodyweight programmes require a little bit more thought though, which may or may not be for some, as because you will be advancing to different, more difficult variations of exercises as you improve, you're effectively the one in control, and it's not quite as simple as putting another plate on the bar like you would do with weights.

Good luck with whatever way you choose to go. As a woman you won't gain muscle as easily as men, so just remember to be patient, and also remember you won't need to run as high a surplus on training days as guys might. As a beginner though, pretty much any decent resistance programme, be it weights or bodyweight training will yield good results

No problem, and don't worry, you don't have to develop visible muscle per se, just re-align the fat to muscle ratio

I found 5:2 excellent for retaining muscle in a deficit. Partly because, if followed correctly, it's a slow weight loss but also partly because the 5 days at maintenance are good for both exercise performance and recovery.
For me the 3 big ticket items to avoid ending up "skinny fat" are small weekly calorie deficit, resistance/strength training and adequate diet where you hit your protein and fat goals.

At maintenance I've recomped successfully, I tried 5:2 but prefer 6:1 (6 days small surplus to cancel out 1 day large deficit).

My opinion on Atkins (or any other restrictive diet plan) would be only do it if you think you can stick to it long term, to me when you are close to goal you should be practicing for long term maintenance rather looking for short term results.