Anytime!

For weighing down the pond liner having an edge or lip about 1/2 meter over the stream with rocks and soil piled on top would suffice.

You could also do an Anchor Trench, you do this by extending the liner out about 2 meters out beyond the lip and dig a trench and put the excess pond liner in taut and fill the trench with heavy rocks and fill over that with soil. This way is extremely secure and you could even put rocks along lip of the stream as well to have it even more secure and prevent kids from trying to get into the stream.

When it comes time for monsoon and rain season, I'd empty a good bit out beforehand and then have a sump pump handy and attach a hose to it to run it out far away from the stream so you prevent the liner from lifting.

Not sure about the specifics of everything you're looking for but I've previously help install a man made pond for a friend. First you'll need to calculate the volume of water your stream will hold, that will tell you how much power you need to run the stream. Side note iI'd recommend putting it away from most trees as the leaves will create more maintenance for you. You'll need a thick rubber pond liner with a nice lip around it, you should anchor the lip and maybe add rocks along it so any overflow won't affect the liner. We put some plants around the pond that help filter the water in the lip that we created, things like bullrush and a couple of other plants. I'd look up similar type plants that are more native to your area and would hold up better.

You'll want install an intake like this at the bottom of your stream and maybe a small pond at the end so the filtration of the pump has more time to work. For extra filtration you could put a mesh box around the intake to reduce strain on the pump/filter. You can also install a waterfall system that includes a filter as well so you'll pick up majority of any algae producing debris.

For any overflow during a monsoon or anything I'd recommend just having a sump pump on hand to pump excess water out and away from your setup.

You'll want to have an electrician out to run some conduit and an outlet for the electronics you'll be using, keep that in mind when planning your run.

Don't add cement on top of a pondliner, cement is way too complicated to work with for something like this as it would need to be reinforced to deal with the weight of the water.

Pond liner can be joined together using seam tape specific to the application.

Yes, because there isn't enough electricity supplied to run both and the lights will suck up as much power as they need leaving the fan with inadequate power to draw from.