You only have a mount when you first spawn in and respawn. They're for getting you to the objective (or further, if you're flanking), not mid-combat. There's also strategy to be had in knocking players off their mounts shortly out of their base, as there's no way to get them back without dying, and thus delays them greatly in their return to the objective, giving your team lots of space to capture. More important in Siege than Onslaught, obviously.
I don't think so, unfortunately. There might be a report button, but I've heard that nothing really gets done.
There aren't currently any chests you can get with coins, no. They're all crystal or promo based. But you can get 50 crystals per week by logging in each day. There's also supposed to be a one time crystal bonus for referring several friends, but I went through that whole process with 7 friends and the rewards system never granted me anything. This was some months back, however. Occasionally there are also "crystal storm" weekends where you earn crystals by getting a win in each queue (Siege, Deathmatch, and Ranked).
Otherwise,
