Question regarding tumblr posts

Hello
My questions is, can i link out my tumblrs to different websites or should i link it to one site only?
If i have A,B,C,D sites, can i link out in every post to different site or should i stick to site A ?
If i link it to one site only, can i place a link in every post pointing to the same site over and over again?
Or should i post one article/picture/video every two months without any outgoing link to make it look more natural?
After how many months of inactivity will be the tumblr deleted?
Some tips would be highly appreciated!
Regards

What I was doing,
If I have Site A B C D
the I create one tumblr account and make post for every sites A B C D and link them to that acount plus I keep their top competitors also.
and created 4 tumblr accounts which seems good ranking on SERPS.

Ideally you need to create different accounts for each website. Just keep adding quality content along with pictures and videos and make links..If possible use other link building strategies in order to index your tumblr link quickly..

I like your strategy regarding ABCD-linking but if I were you, I would get a map to make sure not to interlink in an obvious way.

I would also focus on creating contextual pages so that the more I link, the more context is created that can increase the link value I get from Tumblr.

You can create four tumblr account to obtain good ranking to your web sites and you may add many post with good content and pictures to get result in serps.