Since I am new to agile and as I understand in agile development +
testing + bugfixing etc are done in parallel.
No, Agile does not specify HOW you do things. You are talking about specific Agile practices like Scrum, Kanban, or XP at this point. If you use XP you will do a lot of testing, dev, and bug-prevention in parallel. Scrum and Kanban don't really contribute much in this domain.
If my story is developed , tested, all the bugs are resolved i.e. even
low bugs then only developer start the coding of another story?
This is a good goal to shoot for, but not always possible. Low bugs are sometimes not worth fixing relative to starting higher priority new story work. Other times you will have a manual QA that detects the defect after you thought your work was done. Work with your PO to make the call of whether its OK to ship a feature with a low bug in order to deliver the next item, or if fixing the low item is more valuable to the customer in the given timeframe.
Once all bugs are fixed then only we can submit in UAT or we can
submit with open low bugs?
It depends, work with your product owner (PO) or the customer to see what is desired. Most important is that you openly communicate the presence of low defects in the product so that they can be appropriately prioritized in the backlog of work.
On a side note, UAT is not a requirement of Agile software development. I'd argue UAT is actually a relic of waterfall style development. Practices from XP including TDD and pair programming, along with other concepts like ATDD, BDD, continuous integration, test automation, can all help to eliminate the need for a formal UAT period.