All these statements are incorrect or at least wildy incomplete.
1.VLANs can communicate with other VLANs when they both use the same trunk link to connect to the same layer 2 switch.
No. VLAN separation on the local switch is the same as it is on a remote switch beyond a 802.1q trunk link.
At Layer2, only advanced or strange things can interconnect two VLANs at Layer 2 (as in: they become one broadcst domain). An example could be a "loop" or "ear" cable from one (local) switch port to another port of the very same switch, where one port is untagged VLAN 10 and the other port is untagged VLAN 20.
If one were to build something like that, great caution is advisable: all sorts of "interesting" spanning-tree situations might arise, and traffic flow patterns across the switch might become... a bit strange.
- VLANs with the same default gateway can communicate with other VLANs under the same layer 2 switch
Inaccurate/Incomplete. The term "default gateway" already implies a "Layer 3 thing" being in the discussion.
If that "default gateway" ...
- is an upstream Layer 3 device (L3 switch, a router or a firewall) which has each a L3-Interface into VLAN 10 and VLAN 20 (e.g. 192.168.10.1 and 192.168.20.1)
- the IP networks for VLANs 10 and 20 are distinct (e.g. 192.168.10.0/24 and 192.168.20.0/24)
- the devices in VLAN 10 and VLAN 20 are configured the respective L3 devices' IP address as their local "default gateway" (e.g. 192.168.10.1 for VLAN 10, 192.168.20.1 for VLAN 20).
- the setup on that L3 device permits traffic forwarding ("routing") between the L3-interfaces of VLAN 10 and VLAN 20
... then yes, devices connected in VLAN 10 or 20, even on the same L2 switch, can talk to each other, but with routing by and through the external L3 device. Note that this does not "merge" VLANs 10 and 20 on the local switch.
- native VLAN can access other VLANs under the same layer 2 switch
No. The term "native" VLAN applies to a 802.1q trunk link, where one of the VLANs should be defined as the "native" (untagged). The switch will map untagged incoming frames into that VLAN. The swicth will also talk LACP, LLDP/CDP, and possibly spanning-tree protocols without VLAN Tag on that link.
There are corner cases (Q-in-Q) where service provider and customer need to make special arragements for untagged customer frames, to prevent these from leaking out into the service provider's S-VLAN for that given customer (but a single one).
Other than that: No.