Hello!
Congrats on learning to play! You have set yourself quite a goal.

I'll work on answering some of your questions:
1.) What can help me learn playing pieces with both hands simultaneously.
I suspect you're practicing hands separate and then trying to put hands together at nearly the same tempo, right? You'll need to slow way down -- I mean very slow. So slow that you have time to think about what each hand is doing
before you push keys down. When you put hands together, you are adding another thought process to the mix: where before you were reading one staff, coordinating the movements of one hand, now you're doing the same with two.
You want to go so slowly that you can play correctly, so that you can build in correct sensory memory (touch, muscle, visual, aural). If you go fast, and you continue making mistakes, you'll have a much harder time building the song. This takes a great deal of patience and discipline, to slow yourself down that much. Have courage!

2.) Although I have improved in reading and playing notes.
Time + repetition = memory. MusicTheory.net and eMusicTheory both have free games that will help you do quick note recognition practice (kind of like doing flashcards without another person). Also, take your books and just start reading through and naming notes out loud, away from the piano (you can do the same for naming chords, intervals, etc.) Hearing your own voice , instead of just "thinking" the answers, can help solidify the learning.
3.) Also for sightreading, what is the best way to learn
There was a thread here on sightreading quite recently -- scroll down the forum or do a search. It was a good discussion.
4.) I have difficulty obeying the timing.
Another time to pull out the "slow practice" tool, along with a metronome. Along with a bit of self-discipline!

You can't be in a hurry to play at full tempo. If you give yourself the "time to think" with a slow tempo, you'll be able to navigate the notes and rhythm more easily. Also, know that your inner sense of rhythm will continue to improve the longer you play.
Finally, i have had a lot of criticism from people saying that i might be a little old to pick up piano but i fail to accept this fate.
Good for you! You can absolutely achieve your goals and learn to play piano as an adult. It takes dedication and a willingness to spend time in front of the piano, which you have!! As far as your practice time goes, you'll have to build up your stamina as you go, and make sure you are relaxed and not holding tension anywhere (your teacher can help you with this).
I find that 20-30 minute practice sessions with 10-minute breaks to stretch and clear your mind can be very effective.
Best of luck to you!
Kim