You're unlikely to be able to get enough heat into the bell to do anything useful with a little soldering iron designed for electronics. Small butane torches are not very expensive, so you might just want to buy one.
i’d suggest trying to raise your tongue a bit higher, you can practice by going “sssss” to get a feel of where your tongue can go. make sure not to take in too much of the mouth piece, or too little. keep your top lip firm and don’t let your embouchure fade as you go into the higher register. i’d also suggest trying a different reed if none of these work, and make sure your reed isn’t too hard or too soft. here’s a link to my favorites that helped me when i was having this problem Vandoren CR823 Bass Clarinet V21... https://www.amazon.com/dp/B01HO8L8RO?ref=ppx_pop_mob_ap_share . if absolutely none of these work, contact a band director or stop into your local music store!!! they will be happy to help. hope this helped :D
It tarnish and can be removed with a polishing cloth:
https://www.amazon.com/Yamaha-YAC-1110P2-Medium-Polishing/dp/B01M6C93KN
But also don't leave your case open, otherwise it will attract dust. Make sure you vacuum out the case regularly regardless too.
Get yourself one of these: https://www.qandf.com/rico-multi-instrument-reed-storage-case-with-humidity-control-pack/
Put that in one of these: https://www.amazon.com/Boveda-Humidor-Medium-Travel-Perfect/dp/B019Y7AQIU/ref=sr_1_3?keywords=cigar+humidity+bag&qid=1557521598&s=gateway&sr=8-3 (Or you can show this Amazon listing to your mom or dad and they can buy you one in person)
You'll never have that problem again
I've been a huge fan of Rovners but thought the dark wasn't as nice for solo work. Might want to look at something like the Rovner C3RL Mark III Ligature for your price range. https://www.amazon.com/dp/B000A87OJ2/ref=cm_sw_r_cp_apa_LKgSAbS1565CK