C.W.
My son did this when he was 3 yo. I didn't realize how loud he was and how much of a fitful sleeper he was until we shared a room on vacation. I took him to an ENT who didn't think much of it until he did an Xray of his adenoids and told me that they were the largest he had seen in a long time. After the adenoids came out, the snoring largely stopped unless he had a cold. Everything you mention suggests enlarged adenoids. Get a referral for an ENT.