On a language test, the perfect tense is almost always the correct choice. In general, the word since requires a perfect tense when it means from a time in the past until now, but there are some exceptions in actual usage. Present tense with since. Since that day, the dog walks with a limp. Since that day, everything is great! Past simple with since. Since that day, she came to work for the first time last week. Since I last saw her, my dog died. Since that day we knew we were soulmates.

When it is at the beginning of a sentence, it has the meaning of "from that time onwards ..." , although sometimes it is another way of saying "Because ..."

Sure, you can.

Yes, a lot of native speakers use this phrase at the start of a sentence. For example, since that day I was very careful not to fall over.