YES. I think usually the dedicate one radio to the uplink. The standard AP has two radios, by default one in 2.4GHz the other in 5GHz band. Not sure if newer Wifi standards offer more flexibility while keeping performance. Technical details.
But in general a „wireless bridge“ is a mode many devices support. GL.iNet did a great job to offer this very easy to use (hiding the OpenWRT away).
But you can also use two devices. A wireless bridge (L2) and a router of your choice.
CF is not using „their own“! The certificates the client see must be provided and authorized by the provider of the service. Or put in other words: CF is acting as the hosting provider to the outside, to the clients.
The rest of journey is „inside“ the domain of the provider of the service. It is totally normal that traffic has some journey to go and often it never touches the premises of the provider or even a server owned by the provider.
The important thing that all the part which from a customer‘s view is „internal to the provider of the service“ (behind the CF address) is responsibility of the provider of the service, no matter what 3rd party services they use.
Are you sending lots of mails to a large group of users. If not why not use any normal e-mail service like gmail?
Not at the same time. Both computers will share the 2.5Gb uplink (if this class is supported on the uplink).
What do you mean „access it“? If your TV offers for example to use a media server or a fileserver „type in“ the IP address of your VM provided service. You should know the LAN address of your service before (or is this the question?).
Called „wireless bridge“. Many travel router or home router offer an operating mode for this. You configure the SSID/passwd where the device should connect to. One or more Ethernet ports let you connect your device. (This layer 2, so the device should be able to get an IP from your existing LAN like any other device. Zyxel N300 is good and cheap.
Use an outbound tunnel like the others recommended already.
For curiosity: a mobile hotspot in my mind is a device connecting to Internet via mobile data (LTE, 5G etc) and offering a WLAN. In this case this is your router. But mobile provider often offer no public reachability at all - in which case you are back to the tunnel.
As others said: if it speaks also Ethernet then you can mix. If it just uses Cat cable and RJ45 plugs you can‘t mix.
A simple approach would be to just run an IMAP server. For receiving you use a script using POP3 to download newly arrived emails (which is run every 5 minutes for example). If your server is offline, nothing gets lost.
For the sending side you can either use your mail ISP’s SMTP server directly from the client or you install a local relay as a mitm to the ISP’s SMTP.