Hey Hiro,
From what I'm reading I will write a general response to each subject that you've been told to improve on.
First I will say in my experience you are a nice person who does care about people on the server and the experience of others on the server. I know your timezone tends to make it harder for you to play with other people and I understand that and part of playing SSRP is making money so going AFK to make money does not take away from what you do when you are there. However, it does make you look a bit bad when someone needs your help and you are AFK. As far as appeals go these are usually first come first serve and doing just a few can show how a person will act in doing them from the appeals I've read you are mature and your responses are handled well. As far as teamspeak activity goes it's good to be on as much as possible extending this to contacting LT in my personal opinion I feel it's much better to contact them when theres actually a need to or you are giving actually feedback or thoughts on something contacting a LT member over nothing IMO does not add anything to an applicant beyond the fact that once you are on LT personal relations and communication increase. Moving off that the LT getting to know you is more then just your job it's theirs and it's much easier to connect with someone that you feel is working toward the same goal as you and plus a lot of LT sit in spacers (Me not being excluded from this lmao) so I understand not wanting to contact them for fuck all. I am also aware you are not a brand new admin and you've been admin in the past for about 4 months so this is more then enough admin experience to be accepted for this role. I've talked to you so I'm aware you have some bright ideas. I think you can do well. But as Ezeh said if the LT is not in need of anymore that's just the way it is sometimes. Good Luck.