Okay, I'll give this a go.
1 - Is there a certain Type of Pokémon (Sweeper, Wall, etc.) that is better to Dynamax?
Objectively, yes. Sweepers are far more potent in their Dynamax form than their defensive counterparts. The reasoning here is simple. Dynamax increases the BP of your moves, and has additional effects (Raise in stats, weather set up, and so on), which make it easier to KO more opponents, or at least deal a lot more damage. Consider on the other hand what Dynamaxing does for defensive Pokemon which rely heavily on Status moves: Makes them into Max Guard, basically a glorified version of Protect. And Max Guard can't even be spammed, so it's not all that helpful in stalling. Tanks do benefit to a degree, but you're better off using it to KO as many opponents as possible.
2 - Should you use any different type moves for the added bonus?
Yes, of course. Here's where the secondary effects of Dynamax moves make them complete game-changers and table-turners. Let's suppose you have a relatively slow but hard hitting Pokemon. You can have it learn a damage dealing Flying type move and Dynamax it to use Max Airstream to bump that Speed up so you can carry on effectively sweeping even after 3 turns are up. A great example of this tactic is Fly/Bounce Moxie Gyarados which can now replace Dragon Dance with another damage dealing move. The Max Airstream isn't to KO as much as it is to prevent it from being revenge killed.
Also applicable for weather set up. Specially if you have an ability or team member that benefits from said weather, and you don't want to waste a turn setting up weather. This is a perfectly useful tactic that allows you to maintain offensive pressure by dealing damage while getting that all useful effect that is your actual aim of that turn.
3 - Is it better to have a sand team to support?
No. You needn't revolve your whole team around 1 move that has 1 effect. Just ensure that you have have good synergy among your team members, or at the very least, no damaging synergy (i.e. the opposite of good synergy, idk if a word for that exists). You don't want to hinder your own upcoming Pokemon. For example, if you set up Hail or Sand, make sure you don't bring in a Pokemon with a Focus Sash which will lose the effects of that item.
Similarly with setting up a Terrain, say Misty Terrain with Max Starfall. If your next Pokemon relies on dealing status to your opponent, then you've made your own job more difficult. Just keep testing your teams to make sure you don't trip over your own shoelaces.
4 - One last thing, how much more complex does it get, and how much more foresight is required in Double Battles?
No two ways about it - Double battles are more complicated than single battles. They bring a host of different variables (such as which Pokemon to target). But luckily, the vast majority of Dynamax moves have secondary effects that affect both Pokemon (yours if stat boosts, theirs if stat drops), or all (weather). And since there are more Pokemon at the same time in battle, you have a much easier time in using those effects to maximum benefit (More turns of weather to abuse since you don't have to switch - your partner Pokemon can easily start their offense). Likewise, you can use your Dynamax to raise the stats to make your sweeper do a better job.
Other simple things to keep in mind:
Don't Dynamax right off the bat. Usually your opponent can switch to counter you or at least stall out your turns. Waiting for the right time (recognizing it is a matter of experience) is a lot better, or at least waiting for your last Pokemon (if 1-v-1) or towards the end of the battle.
Note how Dynamaxing circumvents the choice locking of Choice items; Use this to your advantage. Often if you're choice locked and your opponent tries to switch to get you to lose momentum, you can Dynamax to deal damage and raise your stats for 3 turns without losing any turns switching out and around. This gives you the upper hand, specially if the opponent expects a switch. Do note that the choice lock is returned to the originally locked move after you revert.
Dynamaxing defensively can be a strategy useful to stall out your opponent. If they're on a timer (due to Toxic, weather, whatever), and you want to stall them, Dynamax will get you that HP boost needed to survive a potentially KO-ing attack and stall back with your own Max Guard. This is however slightly more advanced and doesn't come up in battles a lot. Most Dynamaxing is offensive in nature. An example of counter playing your opponent. Consider an opposing sweeper at +1 Speed and Attack. You might get KOed in base form. But if you Dynamax and use Max Airstream to raise your speed, you are far more likely to survive - and if you're faster now (since you're at +1 Speed too), you can easily revenge kill and turn the tide of the battle.
Also learn the secondary effects of the Dynamax moves of all the types (or at least, some of the most relevant. Flying for Speed, Fighting for Attack, Fire for Sunny weather, Electric for Electric Terrain and so on). You needn't learn this by rote, but playing more battles will eventually make it easier to remember, since most are type dependent anyway, and all status moves become Max Guard. Sometimes they're not very helpful, so be a little careful while selecting the movesets. Take Focus Blast for example, which increases Attack in Dynamax form - Not very useful when your Pokemon is a special sweeper.