What size seatpost fits the schwinn mesa gsd? what size seat clamP? what size front derailuer? what size bottom bracket?

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Hi, 27.2mm is a standard size for a seatpost, popular sizes includes 30.9mm om newer mountain bikes and 31.6mm on older since it stadardized to some extent. There are still many other odd sizes out there on mostly older bikes.

If you can, get a seatpost that is 27.2mm that fits directly into your frame, with no shim if possible. that will only add weight and creaks.

Also keep in mind that the length is important when you specify a seatpost. You can use websites like this to see what is possible/available before you order:
Seatposts Chain Reaction Cycles

You will also have to consider if you need some setback, if the seat clamp is directly on the post, it is called a zero setback post like this:

Bicycle seatposts are measured in tenths of millimeters. A typical size might be 26.4mm. Because of this you should either A) remove your old seatpost and saddle and bring it to a bike shop or B) measure the diameter of your seatpost with a pair of metric calipers, preferable digital. You can buy them for under $20 from someplace like Harbor Freight. Suspension seatposts tend to come in one (smaller diameter) size and are fittted with the appropriate size shim. Another possibility is an adjustable shim, make just for bicycle seatposts. I highly recommend your local bike shop.

Web search "remove stuck seatpost" and look around. This post has 16 ways to approach it.

http://www.sheldonbrown.com/stuck-seatposts.html

The most secure and sway-free type would be one that bolts to the bike at at least three points, not simply clamping the seatpost.

Blackburn and Topeak make some nice ones. They mostly bolt to those pre-drilled holes above and behind the rear axle and most say what wheel-size bike they will fit plus they have a range of adjustment (usually via bendable metal braces) for reaching that key third point near the top of the seatstays or brake bridge.

Since Iron Horse has gone out of business it is very difficult to find specific information on any one particular model. Their website for resource no longer exists. There is not a standard size for seatposts. There are seatposts ranging from 25.0 to 36.8 and beyond. If the seatpost does not have a head it is a straight post and tapers to a smaller diameter that a clamp goes on (IE. cruiser or BMX seatpost) these only come in a couple sizes and lengths. There are standard posts that will fit but the seat may not match the clamp.

The best method for determining the size of the seatpost is too take the bike into a bike shop. Most decent shops have a tool that they can drop into the seat tube and determine the exact size and then of course offer up what options are available.

The other method is too take in just the seatposts and they can measure those and order off of what you are looking for.

The reason too take in the whole bike is that if you are looking for longer there are additional issues that the shop mechanic can look at and determine the actual seatpost length you will need. If you need a post that is over 450mm long, then you will be very limited in brands and most likely the bike will not fit the rider. That sort of thing.

I have a feeling it is made for old style bikes, not these new fangled things. The seat post clamp is the bolt , nut or quick release that holds the seat in the tube and stops it from going up, down or spinning. In the case of the new bike, it could be way down low, where it won't do you any good. I would suggest a clamp of some sort up top to make the child's seat sit level. Depending on how the child's seat is fastened on, you will have to make something work. Like a pipe clamp, antennae clamp, muffler clamp, something like that to replace the seat clamp. But iof you seat clamp is level or up high, remove the nut and bolt and see what happens with the child's seat clamp. Hope this helps.

Check, clean, and lube all the brake and shifter cables. Check and possibly replace brake pads. Check for any play in the headset ( this is the tube that carries the bearings for the handlebars and front fork ). Clean and lube the chain, gears, and derailers. After all of that just check the torque on all the hardware and make sure nothing is coming loose.

take it to a bike shop and get a new seatpost. bike shops
have manuals that they can check to find a seat post that
fits the bike frame and has the proper size rails to fit your
new saddle.
this is a good time to upgrade the seatpost, you can get one
that is lighter and more adjustable that your old one.