Well, brother it depends on the number of attempts you are having left.

If you are having an attempt left, then you can give JEE advanced and JEE mains and also take part in JoSAA counseling like a normal candidate.

Also, I would recommend you to take part in JoSAA counseling serously, you never know when the destiny falls into your fate. Also, this wold help you in getting a better experience of attending the counseling

Thank You 

Yes sure there's no issue to it you can surely take admission into it. At this stage where you have clearly made it mains if you're rank is good then you may wait for other rounds of counselling as well. If you have good score then you may certainly wait otherwise not 

Hello..

Yes, you surely can.

It doesn't sees whether you have participated in counseling or got seats or not what only matters is that you can give it twice and that's all. Even if you have taken admission in any college, you still can give exam next year.

So, don't worry.

Hope this is helpful.