I want to increase my number of attempts (all sections) and for that I think I ought to increase my speed of solving? Any suggestions on how to increase speed?

solve questions without using pen as much as possible.

Hi, sometimes some questions have direct answers and are very misleading. This I mean in the sense that you might have to work a lot to get the answer calculatively, but most of the time a small glance at the options reveals the right answer. I can show you some examples if you like :)

My quants score is not improving at all. Even after doing all concepts and practicing a lot. It's just not happening. I fee I have some kind of phobia. I just freeze seeing quants.

I feel best way to come out of the phobia is to practice timed quant sectionals, attempt a lot of them don't fret over low scores/percentile for now. Also try to solve all past CAT quants 2017-2020, the quant section's difficulty level is decreasing drastically y-o-y to increase diversity. Pick the easiest of the easiest questions in the sectional and then step by step increase your number of attempts. Remember accuracy is the key. 10-11 correct questions in 40 minutes is above 95 percentile for sure!

The belief and confidence comes with practicing lots of sectionals(In the area in which you're weak). For Quant, before attempting any question, try to map out the steps to solve the particular question. If you're confident about being able to solve it without any hiccups then only attempt it. You should be able ton squeeze out 8 questions in 40 minutes if your concepts are in the correct place. Eventually you can do more questions with consistent test taking.