Should we link our personal stuff with our work computer?
I have so many questions right now.

What would you do if you're in my situation?


Personally I would not load anything terribly personal onto the company owned Mac.  This is especially true if you're loading anything ONLY onto that Mac, as the company likely has no obligation to allow retrieval of the data if you are terminated.


Should we link our personal stuff with our work computer ?


See my last note.  Typically it's not a good idea.  You'll inevitably end up with some personal data on the work Mac but in general I would try to avoid it.


What do I need to consider ?


Consider the right to data on the Mac.  They are providing the Mac to you as a tool for work, unless otherwise agreed on as some sort of benefit.  Consider that their IT team has the right to all of the data on the Mac, whereas you only have the right to your specific data.


Can Admin see messages, emails, browsing history on other account ?


Emails?  Absolutely.  Browsing history? Absolutely.  Messages?  I assume iMessage/instant messenger, they can absolutely see the history (unless cleared) but may or may not be able to use the actual messaging accounts.  Typically though where there is a will, there is a way.  IT folks are very good at finding ways.


Do they have even have the right to see other people personal stuffs ?


Yes.  Because it is stored on their equipment.  Were you give any paperwork when you were hired?  It likely included about statements data ownership with company owned equipment.
Source: I'm the Mac admin for a large nonprofit, overseeing roughly 200 Macs across multiple locations world wide.  We have relatively continuous turn over and as such we regularly access user accounts when people leave or if they are under investigation for improper activity.  It pains me to see some of my users using their Mac as they would a home computer, storing photos, music, etc on them because they will likely lose all of that if/when their employment is terminated. Long ago, to try and make this clearer to the end users, I added a usage agreement (our standard legal data statement) that they have to click through to log in.  It clearly states that the Macs are for work use and that the organization owns ALL of the data residing on the machines and our servers.  This is pretty standard practice throughout the enterprise.
Hope that helps.