1. Adding many characters to initiative with one step requires the API, a Pro perk. That being said, you can use a macro to add any selected token to the tracker. Save this to your macros and click the option to make it a Token Action. Every time you select a token that represents a character, an initiative button will appear. So you won't need to open a sheet.
%{selected|initiative}
2,3. That's a much longer answer than I can give here, but here is another macro you can create like the one in step 1. Any token you select will be able to use it. It creates what is known as a Chat Menu. When you click it, you will get a chat button for the first four actions on the character sheet of the token you have selected. If you character has more than four actions, they won't show. If it has less than four, just ignore the gibberish buttons.
/w gm &{template:npcaction} {{rname=Actions for @{selected|character_name}}} {{description=[@{selected|repeating_npcaction_$0_name}](~selected|repeating_npcaction_$0_npc_action)
[@{selected|repeating_npcaction_$1_name}](~selected|repeating_npcaction_$1_npc_action)
[@{selected|repeating_npcaction_$2_name}](~selected|repeating_npcaction_$2_npc_action)
[@{selected|repeating_npcaction_$3_name}](~selected|repeating_npcaction_$3_npc_action)}} &{noerror}
Here is an example with a goblin:

You can use this principle to set up more chat menus for saves, etc. There are some very good API scripts that give great output, but these require a Pro subscription.