well to start here's a link to the rulebook https://www.yumpu.com/en/document/view/11746153/pdf-rule-book-chaotic-trading-card-game
in case you haven't read it, it has alot of answers to your questions.
buut just to be thorough I'm gonna do em all tooImportant note for all these there is the qualification "unless a card effect says otherwise"
Battlegear- yes battlegear is face down until a creature becomes engaged, there are some battlegear that say it starts the game face up but it will say so on the card, if it doesn't its face down till combat. once a gear is face up it stays face up for the rest of the game.
Energy- one of the most important rules in chaotic is that at the end of the turn, all damage is removed from creatures, also all effects of attacks, mugic, activated effects AND triggered effects also end. so essentially everything is sort of reset at the end of turn.
Turn- a turn starts with a player revealing a location then they move creature, may have a combat, then move more creatures. at which point they end the turn. while there are ways to have more than 1 combat per turn (dread tread for example) usually a turn is 1 full combat.
Mugic effect- as I said in the energy rule all mugic, activated abilties and triggered abilites end at the end of turn (they used to say that on every mugic but later didn't to save space).
moves- each creature can make 1 move per turn, if a creature moves into a space that has an opponents creature in it the two creatures have a combat, the winner stays in the space. you can't start more than 1 combat per turn. you can move your creatures before or after combat as long as you only move each one once per turn.
range/swift- a creature with swift X may move an additional X spaces when it moves, so if I had swift 1 I could move 1 additional space for a total of 2 (it still must be all in one move) . Range only works when paired with swift, it allows creature to move through opponents creature or your own without starting combat if you end your move on an opponents space you still start a combat though.
Defender- if an opponent starts a combat with one of your creatures and a creature next to it has defender you can swap the defender with the other creature and have the defender fight instead. if a creature has a restriction (ex: defender earth) it could only defend that type of creature (ex: creatures with earth)
Mirage- Mirage locations use there normal effect while active just like any other location. however when they become inactive instead of going to the bottem of the location deck there owner can place them on the field on any space (even spaces with creatures in them) the space the mirage is in has the mirage effect but ONLY that space. there can only be 1 mirage on the field at a time so if a new one comes in the old one is put on the bottom of the location deck.
Infection/uninfection- if a danain effect "infects" a creature put a parasite token on it. any creatur with a parasite token is considered infected. parasite tokens count as mandiblors (no matter who's creature there on) when you count mandiblors for various danain cards. so lets say you have 2 mandiblor creatures and your opponent has 2 creatures and all 4 are infected. if you'd have the 2 you control plus the 4 parasites for a total of 6 mandiblors. uninfection as you might guess just removes the parasite from the creature.
Hive- Hive basiclly just a simple switch its either active or inactive. Hive starts the game off inactive but there are lots of effects to activate it (they'll say activate hive) don't forget though that these effects end at the end of turn so next turn hive will be inactive again. if and effect says "Hive: *instert effect here* then that creature has the effect as long as hive is active for example "Hive: water 5" means you have water 5 while hive is active and don't while its not.
stat reset I'm saying this again cause its very important effects of attacks, mugic activated ablities and triggered abilites end at the end of the turn. if its any of those things it ends at the end of the turn.
Strike- strike deals makes the creature do extra damage with there first attack each combat even if that attack did no damage to start, so mudeenus timeslow would do 20 damage in that scenerio
Aqua sheild- when a battlegear becomes unequipped you lose its innate effects which in the aquashields case is the 5 energy (making the heal a bit worse)
Locations- your question is a bit tricky since it depends on the type of effect. remember triggered abilties aka. ones that happen at a certain time, last till the end of the turn even if the location goes away in the middle, look for phrases like "at the beginning of combat" "when this becomes the active location" ect. innate effects of locations are only on as long as the location is active. they WON'T have a specific time they'll just have an effect ex "engaged Creatures have exhuast courage 5" "Creatures have fire 5" "creatures may only play generic mugic" ect. those type of effects will go away if the location changes mid turn. \\
proboscar- as you said proboscars first effect is easy to understand he can move to any open space. for his 2nd effect remember that the way to start a combat is to move your creature onto the space of an opponent creature. normally this puts you on there space and you fight for who stays there. with proboscar when he moves onto an opponents space he instead pulls that creature onto HIS space and they fight there instead (this effect is useful for pulling creatures away from defenders or to a spesific spot)
hopefully that clears things up again I'd give the rulebook a good read and if you have additional questions after that lemme know