Is there any way to know how much length diff or gap should be there in the heights of the handle bar and seat because obviouslymy child seems to have problem riding the bike for long and I am not able to find the cause for the discomfort.

Check the chain the goes between the handle and the flapper.
It should not be taught. If it is it will not permit the flapper to seat
properly and water will leak out. Adjust the chain length so the flapper is seated and there is just a little slack in the chain.

The problem is the forward controls and the handle bars combined not just the bars.

The problem will never be fixed just by fitting bar risers that will take some pressure off your wrists , but realistically there wouldn't be much there anyway because of the seating position on the America.
Might be time to start looking at a different bike.

this bar stool can be adjustable the height. You can operate it by the handle under the seat.

Hi
Undo the popper on the shoulder harness pad. Slide the pad down the length of the shoulder harness strap.
Unhook the metal D ring.
Feed the short length, low down anchor point back in behind the seat fabric. Bring the longer length, higher up anchor point out at the desired height.
Re-attach the D ring. Adjust the harness straps accordingly.
Slide harness pad back up shoulder harness and re-attach popper.

you could try a little bit smaller rear tire. cheaper than the shocks maybe

You need to pass the belt behind the sit.

I am not sure which question to answer, so I will try both.

raising the handlebars, loosen the stem bolt 4or 5 turns, (this is the bolt on on the top of the handlebar stem). Tap the stem bolt with a hammer, the bold should drop down and the handle bars should fall loose, adjust as needed, then tighten the stem bolt to set.
Please note, there is usually a limit line on the stem, do not raise bars above this level as iy will make the handle bars unsafe and could pull out or break off.

second question, Child seats ar very adaptable, an will fit most bikes. Be sure to use all the necessary hard ware and safety guards. for you and your passenger.
Try to get the seat set up as low as possible as the higher the seat the higher the center of gravity. It will have less effect on handling characteristics if you keep the seat low.

I hope this is of some help.
Ed

I know this is months later, but here you are in case you (or anyone else) needs the info again. First, though, I feel that it wouldn't be responsible to neglect to tell you that if you got the seat in 2000, it is expired and no longer safe to use. Car seats generally expire after 6 years because the plastic degrades over time - in a 10 year old seat, it can look fine but actually be brittle enough that the entire harness can rip out of the seat if it's an accident. For the manual, visit Cosco's website and fill in the product number and date of manufacture. It will bring up a PDF file of the manual that you can download. To rethread the straps, first replace the **** strap. Slide the metal plate down through the slot in the seat, with the buckle facing out. Slide the metal clip under the tab and push it down to lock it in place. Facing the seat, start by threading the end of the harness strap down through the slot of the left side of the bottom (where the child's right hip would be). Under the pad/cover, thread it across the bottom of the seat and up through the matching slot on the right side. Pull it until you have equal lengths on both sides. Thread the buckles onto the the strap (one one each end) and buckle them. Thread the chest buckle onto both ends, making sure that the harness doesn't twist. Buckle it, too. Push the ends through the harness slots. Pull the harness through to the back, making sure that it goes OVER the metal bar, but UNDER the plastic adjuster handle. There is a loop sewn into each end of the harness. The adjuster strap has a splitter plate, kind of shaped like a Y. Slide each loop over the ends of the plate and all of the way into the slot, so that the curved ends of the splitter plate are exposed and the strap is secure in it's slot. Adjust the harness height by squeezing the metal bar on the back of the seat (the one behind the harness) forward and moving it and the plastic adjuster bar up or down to the correct position (at or below the shoulders for rear-facing, at or above the shoulders for forward facing). Do note that the very top slot is NOT for use with the harness - it's only to adjust the headrest when the seat is being used as a seat belt positioning booster and is not reinforced to support the harness in an accident! Adjust the tightness of the straps with the button/extra length on the front of the seat. Properly tightened straps should lay in a straight line without sagging and you should not be able to pinch up any slack (lengthwise going down the harness, not across the width of it) at the shoulders or hips. Adjust the chest buckle to lie in line with your child's armpits, never his neck or belly.

Hi guys, I had this problem when I first got my urban rider - the trick is to put the seat on correctly in the first place. If you look under the front of the seat (when seat is facing away from mum/dad) you'll see 2 plastic hooks - these need to be hooked over the first horizontal bar of three that you can see (it has a small black plastic nobbly bit on it) then, as you were doing, push the handle and pull the 'tube'. If the seat is facing you (child travelling backwards) it won't fold, neither will it fold with the carry cot attached.
Hope this helps! Tegans mum x

Hi guys, I had this problem when I first got my urban rider - the trick is to put the seat on correctly in the first place. If you look under the front of the seat (when seat is facing away from mum/dad) you'll see 2 plastic hooks - these need to be hooked over the first horizontal bar of three that you can see (it has a small black plastic nobbly bit on it) then, as you were doing, push the handle and pull the 'tube' on the left. If the seat is facing you (child travelling backwards) it won't fold, neither will it fold with the carry cot attached.
Hope this helps! Tegans mum x