If a new player starts the game as a Ratcatcher, does their SbVD also get two free Trick cards? Much like Wizards and Priests get free spells and such? Or must the Ratcatcher player spend their purchased talents to manually buy those Tricks?
I'm quite certain the Ratcatcher doesn't get any free tricks. Page 156 of the Player's Guide repeatedly states they start with "two Trick talent slots" (emphasis mine, but the original text says slots not cards) and goes on to say that "You acquire Tricks just like any other Talent cards." It also says Pet Actions must be purchased with Advances.
On a related note, page 39 of the Player's Guide clarifies that Initiates (Rank 1 Priests) do not necessarily start with free spells and actions. They only get them if they spend character creation points on specific advanced skills. They included an updated sidebar in the Player's Guide to clarify what free cards Wizards and Priests get, but that sidebar makes no mention of Ratcatchers getting anything free. I take that absence as further confirmation that Ratcatcher's get nothing free (except the Dog itself, which is clearly stated on the Ratcatcher's Career Ability card and on pg 156 of the PG).
However, the card says you pay for both talents and actions the same as regular.
Your Small But Vicious Dog may learn Tricks talents that socket into this Follower sheet. You acquire Tricks just like any other Talent cards. Your Small But Vicious Dog also gives you access to Pet action cards, which you purchase with advances.
So the argument in question is whether to treat the basic pet action cards the same as the basic spell or basic blessing actions.
What "basic pet actions" are you talking about? I just looked at the cards that came in my Player's Kit, and their corresponding entries in the Player's Guide, and none of them have the "basic" keyword.