There are a couple of things I would change…
drop this part from your pfsense config:
Then I configured the pfSense as following. I created another gateway with the ip of 10.10.1.10 and called it LANGW. Then I created a static route of 10.10.2.0/24 using gateway LANGW. Then created another static route of 10.10.3.0/24 using gateway LANGW
Add a IPv4 static route in the cisco switch:
Destination IP Prefix: 0.0.0.0 Mask 0.0.0.0 Next Hop: your pfSense LAN address
(it tells the switch -who is doing the inter-vlan routing- to forward all traffic that didn't hit the local route table to the next hop address)
Then add the different networks in pfSense, under "System\Routing -> tab Routes" (only the 2 other subnets in your setup, they are currently unknown to pfSense as there is no routing protocol running (?))
Next, but equally important, you need some instance to resolve the name, so you could configure the switch to send DNS requests to pfSense (found under "Domain Name System\DNS servers")
Not sure if this will work though. Alternative: configure the LAN ip of pfSense as DNS server IP in your clients.
That should give you internet access (unless I'm forgetting something ;D)
Last, fix that vlan setup. Trunks are only required if they need to transport vlan information (802.1Q). If no trunking is required, I think it will be better for your setup to configure the port to access.
Easiest fix: assign those ports as "access" to the correct vlan (menus "Port to VLAN" and "Port VLAN Membership" and set the native vlan back to 1 (pvid))
An alternative to this setup, would to configure your LAN interface in pfSense to also do trunking, but then you would need to configure those vlans also in pfSense and let pfSense do the routing instead of the switch. Not more complex than your setup, just another approach…
Good luck & let us know how it goes... ;)