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You need a checklist. Keep building a checklist as your experience goes up.

After you complete a work, spend 30 minutes more in ticking off the checklist.
Yes, make checklist of the mistakes you're doing.

And before submitting your work, see whether all the points mentioned in there are complied or not.

Don't try to remember things, instead note them down.

It helps a lot.
It gets better as you spend more time working - don’t worry
Why don’t you talk to seniors after you do some work and understand how you can improve and what are the things they would look for.
There is no such thing as “cut out for it”. If you stick with it long enough you’ll master the process. Just try to be more alert and less hard on yourself. Sab log ek jaise nahi hote. Have to allow yourself a learning curve also.
Think you’re reading too much into your partner’s silence. Partners tend to have so much to do that they don’t have time to give feedback - no feedback is good feedback.
Understand the work, look at it from the client's perspective, don't work to impress your senior, forget about him, work to solve the problem instead. You'll stop making mistakes.
You managed to get through an entire post without a single typo! I'd think you're better off than the large majority here. Don't let it get you down.