Free WiFi is available at over 104 stations across the Thameslink network. First Class tickets are available but not all Thameslink services offer First Class seating. Only folding bikes are allowed to be taken on to Thameslink services. Non-folding bikes generally can't be accommodated on services into and out of London during peak times. As per the National Rail Terms of Carriage, up to two small pets can be taken on board for free, providing they do not take up a seat. Additional pets will require tickets. Usually they will need to be kept on a lead or in suitable pet carrier.
Find a PDF version of all Thameslink times here.