1) Which peace of equipment would you advice buying first: regulator, diving computer, BCD?
2) Would you advice buying Seaquest libra BCD for 150 dollars for use in tropical waters and in freshwater cold lakes?
3) What is 5 mm full body wetsuit suitable for?
I'd go for the computer first. You can always rent a regulator or BCD, I haven't seen too many places renting computers. Also, many computers keep a log of your dives, which you'll find to be a great record. You should never rely on someone else's bottom timer or gauges. What if you get separated?
Not familiar with Sequest Libra. I have dive friends that use Seaquest, so I wouldn't have any concerns about the quality of the equipment. Of course, make sure it fits good, with your wet suit underneath. From a website, I can see that the Libra lets you put half of your weight in the back where it's non-dumpable, which I think is a great idea. It's also is rear-inflating, which I personally prefer to having the bladder wrap around my side. Finally, it has D-Rings, which are good for attaching your gear to. It certainly looks like a good design for a BCD, assuming it fits you properly.
If it's been sitting around unused for 4 years, I'd make sure the inflator and dump values all work properly. They're replaceable if necessary, but you might as well know before you buy what maintenance might be needed.
I don't like to travel with a wetsuit because it never seems to dry out in time to take it home, so I pretty much rent a wetsuit when I travel.
I'd buy a wetsuit to use where I intend to dive the most. For 21 degree water, I'd personally go for a 7mm. I'd be cold in a 5mm after half an hour at that temperature. But, I'm 56 years old and not as tolerant of cold as I used to be. Of course, the wetsuit has to fit good in the first place, or it won't do you any good.
I hope to go diving in the Red Sea next year. Have a great trip.