I assume you are looking at Tallink-Silja? I travelled last winter with one of the Tallink ferries in Business Class. Nothing spectacular, in terms of food and drinks, but quite comfortable as the area is quite calm. I would say it's worth the money. The more you eat and drink, the more you save

No immigration in Tallinn anymore when you come from Helsinki. It's all the same Schengen area nowadays.

You can buy tickets in advance, and as you are taking a Friday evening departure, it might be good to buy the ticket in advance. Else you risk the ferry and business class being sold out.

Tallinn is a fairly small city. I took a taxi from the ferry terminal to the airport, and it was much under 10€. I don't remember the names of the taxi companies, but sometimes you hear about people who have been ripped off by taxis. Use common sense, i.e. insist on a meter and keep an eye on it, or agree the price in advance. I would say you should be able to go anywhere within the city centre for 10€, probably much less.

I don't know where the hotels you mention are, but the city centre is a 20-30 minute walk away from the ferry terminal.

Hope this helps!