What might be the issue with my car, and how to fix it possibly?

Alright so two things are happening with my car which I m assuming are going to be annoying to fix and expensive, but I m hoping that they aren t adn maybe just small things that I need to do.

My car is a 2002 Honda Civic DX
it has 136,000 miles on it
I just replaced the timing belt (before it broke)
the alternator (battery light was flashing on and off occasionally, but only happened every few weeks)
AC belt
Oil change
Spark plugs

Alright so both of these things only happen some of the times not every time, and they happen weeks apart or even a month or two apart without doing it again.
But I want to fix whatever s wrong before it gets worse adn I get stranded somewhere.

1st thing.
When I first start my car, occasionally some of the times once I start driving from the initial parked spot, it starts going and then seems like it dies, it doesn t accelerate, but then when I press down on the gas a little more, it goes just fine. It s only done that to me 4 times now and I ve had the car for months. However that is a big issue that I need to get fixed before it gets worse. If anyone knows what might be causing that and any remedies to get it fixed or what the issue might be, please let me know.

2nd thing.
This only happens occasionally as well, it seems to happen more often when I m going up a slight incline compared to regular driving.
The acceleration goes and once it gets up to a certain gear it revs up to in-between 3 and 4k RPM when it was in-between 2 and 3k RPM s
Added (1). so more on the 2nd thing (ran out of room) it jerks the car then settles back down to in-between 2 and 3k rpm's.

This problem seems to happen more often when going up a slight incline and from a stopped position going up to 45 or 60. It also happens more often when the car hasn't been running for long that day. It happens less often when the car has been driven a bit.

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