Yes, you can safely buy and play all the DLCs (assuming you're on a PC/PS4/XBOne). Trespasser was the last DLC. As for which order to play them, technically you could do Descent and JoH anytime during the game or afterwards but they are level gated and Trespasser in post-game DLC only. Descent is more or less aimed at around level 15ish. You could maybe go around level 12-13 but the battles will be interesting. I did that once then left and came back later. I tend to do Descent after finishing Adamant & Halamshiral now. JoH asks for much higher levels. We're talking go there at level 20 and you're going to struggle. Both Descent and JoH can be done post-game but you obviously won't have Solas so if you want to take him, go before the end.
A lot of when you do them depends on how overleveled you want to be for the final battles. If you do Descent and JoH during the game and you've been reasonably but not entirely completionist in all the regions, you'll probably be around level 26 or 27 (which is the level cap) when you fight Corypheus, which makes that fight very short.
As I mentioned above, Trespasser is post-game only and when you start it, you won't be able to go back and complete anything you've left undone.
Also, with Trespasser, you get the Golden Nug, which allows you to transfer schematics, thrones, banners etc between characters and you get the Golden Bug from the moment you get to Haven. You also get the wardrobe, which lets you get out of the beige PJs in Skyhold.