Next, you have to make sure that you have assembled everything correctly. Yes, telescopes made in China do have a poor reputation, but then, they are inexpensive. And, most of the time, as long as the main lens is OK, then you can often salvage the rest with a bit of work.
Do set up the telescope (outside if you can) during the day when you can see what you are doing, and make sure everything that can be screwed in, is screwed in at the right place, and solidly. NEVER use the scope to look at the Sun (in fact, never point it to the Sun, even if you don't intend to look through).
In inexpensive telescopes, the finder scope is rarely dead centre. However, as long as the finderscope is steady (and as long as the target is in the finderscope when it is also in the main telescope) you can always use it. You do get used to reminding youself, every time: I have to place the target one-third of the way towards the left. If the finderscope is steady enough to do that, then it is a useful finderscope.
An equatorial mount SHOULD move smoothly. However, some models do have a "stop" at the end of the travel. This means that you should be able to rotate freely (by unlocking some kind of a pin) and "unwind" a thread - the one that is supposed to move the telescope slowly as you observe - so that it is not at the end of its travel.
On my small scope, it normally gives me approximately 10 minutes of observing, then it reaches the end and stops. I have to unlock the mount, unwind the fine movement screw, recentre the telescope on the target, relock the pin, and I then have another 10 minutes of observing.
Of course, for projects where I need more than 10 minutes at a time, I mount the small scope on the larger telescope (as if the small telescope was a finder scope for the big one) and I use the motor drive of the big scope.
Finally, the best tool you could get to check out your telescope, is a friend who has experience with telescopes...
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PS: small telescopes are OK, as long as you use them (and as long as they are usable). My small 80-mm weighs only a few pounds (barely more than 1 kg) and I can set it up in 5 minutes. The big beast takes almost an hour to set up and weighs close to 60 pounds (around 25 kg).
If I want to just enjoy a quick view of Jupiter's satellites or of the Moon, guess which one gets used the most...
A small telescope that you use, will ALWAYS be better than a big scope that sits un-used, in the basement.