Is my hamster going to die? (Syrian 2.5yr)?

Your hamster is lucky he has you as an owner as you obviously care about him so much, but I am sorry to say this but it just sounds like he is coming to the natural end of his life. Syrians live on average around 2 to 3 years so 2.5 is a ripe old age. My last hamster started to behave just like yours and ped away within a week. Just in case though I would try maybe buying a fresh bag of hamster food as once they have been opened hamster food does start to lose its vitamin and mineral levels. It is possible he is tired and losing fur because of a poor diet. Also try a different type of bedding and maybe a different substrate to sawdust in case he is allergic to one of them and that is making him sneeze. I would prepare yourself for the worst though, but don't be too sad, it sound like he has had a wonderful well cared for life.