What could I resolve with my Telescope I recently won a Common 50mm refracting telescope with Solar Filter too.. I'm trying to Understand things I can skygaze with it. It's pretty basic and I should have known. Unfortunately, I don't possess this knowledge now. I had searched on various good websites which detailed and other requisite! Given, I stay in Navi-Mumbai, India, and less cloudy and less dusty area, what would my telescope's eye see? 

And how to maintain and keep the Telescope in a good state.

What things would make me a better amateur-observational-astronomer?
The Moon is the easiest target to start with.
After that, try whichever bright planets are currently in the sky: Jupiter, Saturn, Mars, Venus.
Then get a star map and try to find some of the brighter star clusters, nebulas, and galaxies.

I recommend the monthly sky maps and object lists at Skymaps.com.
Latitude 19&deg;N falls midway between their northern and equatorial editions, so try the equatorial one and remember that your southern horizon hides the southernmost ~10% of the map.
Most of the "Easily Seen with Binoculars" list are also good targets for a 50mm telescope.
Objects labeled e.g. "M42" are in the Messier catalogue.
Some objects are easier to find with a more detailed star atlas.

A telescope calculator indicates that in ideal conditions, 50mm aperture can theoretically show stars as faint as magnitude 11 or resolve double stars 2.5 arcseconds apart.
In practice it's reasonable to try objects as faint as magnitude 9 or as small as 4 arcseconds.

If the telescope has a finder or other aiming device, check its alignment periodically.
No other maintenance is required if you store the scope in a clean, dry place and use the dust caps to protect the lenses from dust and fingerprints.
A few specks or spots will not significantly degrade performance.
Only clean it if it gets very dirty, and then take care not to scratch or strip any lens coatings.

As you learn your way around the constellations and acquire more challenging targets, you can sharpen your observing skill by keeping a journal in which you describe or even sketch what you see.
A local astronomy club can give you ideas for observing projects and opportunities to try more advanced equipment.

Solar safety note: filters installed near the eyepiece can overheat and break; filters which securely cover the whole objective and make everything else invisible are usually OK.
With a 50mm aperture, the eyepiece projection method is a good alternative.