I have a 2 story house and about 20 years old. I recently bought this house.
I do not know so much about to maintain properly.

I have a delime that, when I put the thermostat to 70, the downstairs always get cold but the upstairs get hot. As long as the hot air comes from room vent, it feels warm and I tried to put the thermostat to 65, it gets cold in a short time, this happens only downstairs.

I checked if there are any leaks in the windows, doors etc, I did not see any, But I found cold air coming from Chimney, I closed the chimney cover but still air comes from inside.
I covered the chimney from outside with trash bag, helping little not much.

My questions are

Anybody know if there is any material I should use to cover chimney because I don't use it.

Is there a way I can check if the house is reasonably air tight, if not where and how to check?

Thanks

If you plan to never use the chimney, you can have the top sealed by a bricklayer. If you do want to use the fireplace, consider installing a wood-burning fireplace insert, or a gas fireplace. Both will be sealed and burn outside air, so they won't be paths for warm air to exit your house and cold air to come in.

I would also suggest checking the outside walls to see if they are insulated. Take the cover off an electrical outlet and look into the tiny gap between the metal box and the drywall. You should be able to see some insulation in there, behind a sheet of plastic. If you don't, well, it might go some way towards explaining the cold.

Other areas to look for air leaks? Weatherstripping around doors and windows are big leakers. If the weatherstripping is old or missing, that could lead to drafts. Another big spot for air to leak out of your house is through the attic hatch. It should be fairly heavy, and rest on some weatherstripping. It's also good if the hatch is insulated with some styrofoam. There are companies that will come in and assess your house for about $300. A reputable one will be totally worth it.

One final question for you - is the thermostat upstairs? Heat rises naturally, so if the upstairs gets warm first, the thermostat will notice that and shut the furnace off. If the upstairs is heating up much faster than the downstairs, you should be able to re-balance your heating system. Down in the basement, there should be louvers in the heating ducts. Just close down the ones to the upstairs vents, and open up the ones to the downstairs vents.

Good luck!

Take a look at www.thermaview.info