Can I work on old manuscripts using personal time? I submitted few manuscripts to some journals during my PhD and moved to other institute for postdoc (full-time) in few months before. Now one manuscript has come for revision and other manuscripts may come soon. I have following many questions in my mind. 

I am wondering is it ethical to spend some time to make revision of my old manuscripts in holidays/weekends in my house without using any resources from Institute?  

Should I need to discuss this matter to my present supervisor or Institute?

Should I acknowledge my present Institute? Is it also necessary to change my affiliation?
Let's address your questions one by one.


  I am wondering is it ethical to spend some time to make revision of my old manuscripts in holidays/weekends in my house without using any resources from Institute?


What you do on your free time is entirely up to you: no job, boss, or conditions, can take that away from you...

(Well, almost… as noted in comments, there can be clauses that limit your abilities to work on other projects, but I would think that the principal case in which it causes problem / conflicts of interest, is when that "side activity" is paid, which, I assume, is not your case.)


  Should I need to discuss this matter to my present supervisor or Institute?


...yet, depending on the sensibilities and particular conditions of your employment, you may want to tell your supervisor. You don't have to make it super formal, as it is rather usual for a young post-doc to have ongoing work that follows publications made during the Ph.D. Just mention that you'll be working on some revisions on your free time, and that should be fine.

If your supervisor shows interest ("Great, you should make a presentation", "Tell me more", "What are the connections with our current project?"), you can try to make fruitful connections, but that may not arise.


  Should I acknowledge my present Institute? Is it also necessary to change my affiliation?


I would think that this will depends on the country, institute, kind of supervisor, and many other aspects. Listing your former institution as the "main institute", and your current institute as your current address would probably be the safest option.