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It might help you to try using the telescope on a distant object in daylight (eg a tree or building on the horizon), as it is a LOT easier to work out how everything works with a nice bright terrestrial target. If it goes slightly out of focus, or changes alignment slightly, when you change eyepieces or add a Barlow (e.g. the different weight of the two eyepieces can make a difference to the exact aim of the telescope), you can generally make out some sort of image, and easily work out which way you need to refocus or realign for the new eyepiece.
The 25 mm eyepiece will give a lower magnification view, and the 10 mm eyepiece will give a higher magnification, somewhat dimmer view. Generally, both eyepieces should be roughly focussed at the same settings, but you generally need to do some refocussing when you change eyepieces. The Barlow will increase the magnification of any eyepiece, but will also reduce the brightness, and you may need to refocus quite a bit when you swap the Barlow in and out.
In general, the low power eyepiece is the easiest to use, so get fully familiar with that, and then experiment with the 10 mm, then try the 25 mm and the 10 mm with the Barlow.
I would guess that your target (Jupiter) was slightly out of view when you swapped to the higher power eyepiece (and possibly also out of focus). This is where experimenting in daylight can help - even if the image shifts a bit, you can easily work out what you are looking at; with a single small target, when it is out of view, and slightly out of focus, you may see nothing, and may not know which way you need to realign and / or adjust focus etc.
The Finder Scope should clamp reasonably firmly in the mounting bracket. Try making sure all three thumb screws are reasonably firmly tightened - but don't overdo it. But yes, some small finder-scopes may wobble a bit in the bracket.
(Note on terminology - the small "piggy-back" scope you use to aim your main telescope is the Finder Scope; a Spotting Scope generally refers to a small stand-alone telescope designed for terrestrial viewing.).
For batteries, try getting 8 x AA rechargeable NiMH batteries - they should get you though a couple of night's viewing pretty easily, and you just recharge them instead of throwing them away when they are flat. Yes, you can also power the mount using a cigarette lighter lead from your car, or from a car jump starter. You can use pretty much any 10 volt to 12 volt battery, but don't try to hook up anything with more than 12 volts, and make sure you get your battery polarity right - if you get the polarity wrong, you could fry the mount in an instant.
Hope this helps!
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