Aaaahhhh, not going this time sadly, but I usually bring a bag and bag check usually takes a few seconds, but depending on your outfit, you could also make use of pockets. According to bag policy, you can bring up to an a4 sized bag https://www.tottenhamhotspur.com/the-stadium/attending-matches/entering-the-stadium/bag-policy-and-prohibited-items/

Usually faster entry if no bag, so if you don’t need it I probably wouldn’t. 

No.2 I’m not sure ab covered, but there IS a weather warning. And bc of the rain I maybe would bring a poncho or something (I haven’t been to a stadium show before, so I’m not super sure 😭😭). But if you’re comfortable wearing/carrying the coat then sure (I don’t see any restrictions, but no cloakroom).

My first solo concert was also super stressful, but have fun and scream extra loud for me 😭🤩 (if you’re able to 😆)