1) Getting to Algarve from Lisbon (my flight should arrive at 3pm 10/05 Fri), should I get the evening bus or train to Algarve?
Ticket prices for train and bus are about the same, but if you are heading for Albufeira the railway station here is about 6km out of town, so you must add the cost of a taxi (about 8 Euros) or bus (€1,40) to the equation.
The RENEX bus line (www.renex.pt) uses the Lisbon bus terminal called Gare Oriente, which is much nearer the airport than the alternative.
The Rede-Expressos / EVA buses leave from the Sete Rios bus terminal in Lisbon, which is 30 minutes by metro train from the airport costing about 2 Euros, or a bus will take you there for €3,50 or taxi of course.
Trains leave from the Oriente railway station, which is next to the bus station of the same name and about 5 minutes by metro from the airport.
Reservation is essential for train or bus. Fridays from Lisbon to Algarve are very busy in terms of people travelling.
2) Albufeira is very touristy in summer, but in mid-May there are will not be many tourists around. Lagos is a better town from the scenic point of view but there will be less to do. Lagos is also popular in summer.
3) Not sure what you mean. The bus journey Lisbon to Albufeira is about 3 hours. They run non-stop part from a 15 minute rest break en route. The trains are slightly quicker but do make several stops along the way.
4) Perhaps you can give us an idea of your budget and requirements. there are literally hundreds of hotels, apartment hotels etc etc.
You can easily stay in one and visit the other. There are buses and trains between Lagos and Albufeira several times every day. The bus journey is about 90 minutes.