Those are probably fine (I've never used those particular ones). Looks like they may have a tripod adapter built in. If so, that's pretty good, as those might be a little difficult to hold steady.

I absolutely agree with the other comments about going for binoculars over a cheap scope. Go for binoculars with big objective lenses and don't go for huge magnification. While you want some magnification, what you really want is to get more light into your eyes. With binoculars like that, you should be able to see lots of interesting and beautiful things in the sky. You may be able to find an old pair in a second hand shop... Goodwill for instance?

As for telescopes, you won't find anything that won't frustrate you terribly for the kind of money you're talking about. I got a department store scope when I was a kid, and it just drove me nuts. You might look into making one. One of the popular telescope designs is called a "Dobsonian". It's a simple telescope, often made from cardboard tube and plywood, with a home-ground mirror. They are named after the guy who developed the design, John Dobson. He used to make these telescopes and take them out in San Francisco and show the sky to local kids. Sometimes, he'd give one away to an eager kid. He was a monk (if I remember right) and had to make them cheap.

Look around your area and see if there is an amateur astronomers' club around. If so, there are bound to be old codgers there who would be helpful with advise on getting into astronomy, what sort of equipment might be good, and how to make your own, if that sounds interesting.

Don't forget, by the way, that you don't have to have expensive equipment to get into star gazing. You just need at least one eye and clear skies. Although having a star chart with you (either printed or an app) would be a big help too. Binoculars and telescopes will show you more, but there is a lot to see just by looking up.

My first recommendation is to get a multimeter, if you don't already have one, and check the voltage on those wires coming off the fan when the fan is running. LEDs have an operating voltage. That is, when an LED is lit, there will be a particular voltage drop across the LED. The exact value depends on the details on how the LED is made, but a typical white LED will be around 3 volts. If you put a white LED in parallel with a fan, and the fan needs 5 volts to operate, the LED will end up clamping the voltage to 3 volts, and the fan won't run. (The LED will also run pretty hard and won't last long.)

One important thing... are these inflatables battery operated or powered off the mains? If off the mains be SUPER careful about the wires when you check the voltage. Treat them as if they could be live. While the voltage might be 5 volts, you don't know if there is proper protection on that, and you could get a nasty shock off them. Don't touch the wires while the thing is plugged in, and don't let them come in contact with each other or anything conductive.

So, check the voltage across the fan and see what it's running at. I'd guess it's running at 5 or 6 volts or possibly 12. If it's 5 volts, put a resistor (100 ohm 1/4 watt should be fine) in series with the LED and the two of them together across the wires:

WIRE----RESISTOR---LED---WIRE

If it's 6 volts, you can do two LEDs in series (maybe with a small resistor in series as well):

WIRE---LED---LED---WIRE

If it's 12 volts, you can try four in series. Make sure the LEDs are wired in the same way, since they're polarized.

Another possibility is to get LED tape. You can probably find LED tape that will match the voltage of the leads without much fuss.

Finally, you can order resistors online. I don't know what country you're in, but in the U.S. you can order resistors from various places: Adafruit, Digikey, Mouser. You can even get starter kits that have various resistors in them.

EDIT: After I posted this, I got to worrying about my response. Frankly, if these things are powered off the mains, I wouldn't recommend messing with them. It isn't just the shock risk while you're working on them, it's the risk of a short and/or fire while they're operating at night. They'll be outside, where they could get damp and so on. That's really not a serious problem for something that works off batteries, but for something that's mains powered, it could turn bad. You want to be sure of what you're doing before messing with something like that.

If you don't already have one, I'd head down to the local hardware/homegoods/electronics shop and pick up a multimeter. First thing to try is to use the DC voltage setting and check the leads going to the pump when you think it should be running and verify that it's getting 12-ish volts. The main thing to figure out first is if the pump is burned out or if the problem is "upstream" of that.

I don't think you really have a problem with the solar panels or the battery, because it looks like from the controller display that your battery is fully charged to around 13 volts... which should be fine. But I'm making assumptions about what that display means.

Possibilities that occur to me:

• The pump motor is burned out
• You have a defective lead going to the pump (you can use the continuity mode on the multimeter to check that)
• A transistor blew on the charge controller (one possibility is that the controller is not designed for driving motors... when a motor turns off, it can generate a big spike of power back to the controller... if the controller is not designed to handle it, it could damage the circuit).

EDIT: On the multimeter: you don't need a super fancy one. Even the cheapest should have DC volts and something to do a continuity check. A more sophisticated one will be more useful for other projects, but it's not like you need an expensive meter that measures down to the milliohm and can whistle the Star Spangled Banner.