If I have an amp(Vox AC30 for example) and an output jack in the back of the Amplifier, can I connect this jack to a sound card or a mixer and record everything that go out from the amp (feedback too?) What is going out form this jack?
Different amps have different types of line-out. An early modification for Fender amplifiers was to fit a 'tap' out of the preamp, by splicing an output between the preamp and power amp sections. Before master volume controls were standard this allowed a Fender amp to be run at a cleaner setting, and then bolstered to concert volume using another power amp.
Some amps have line-outs that emulate a speaker cabinet, and companies like Palmer make speaker simulators that can be inserted between amplifiers and speaker cabinets to allow a DI feed to be sent to the Front of House, modified to mimic the tone of a mic'd up speaker cabinet.
For feedback you need to find an output on your amp that is strong enough to drive recording equipment and doesn't mute the speaker(s) in your amp. Feedback is the almost organic interaction of guitar and speaker, and doesn't happen without the two in relatively close proximity. A simple cheat may be to split your guitar signal into a second amp, running at a higher gain setting. Your first amp is feeding your recording interface, and the second amp is primed to produce feedback. Assuming that you want feedback from the strings, and not simply the squealing microphonics of a pickup feedbacking internally, this method might work quite nicely though it may sound more like an Ebow than anything else.
You can if it's a line out jack, as it will be a line level output and is made specifically for the purpose of taking the output of the amp section (not cab) and connecting a different cabinet or recording etc. Be careful that you select the appropriate line level on the interface, or Bad Things could happen (most likely a weak signal, worst case a damaged input)
Depending on if the power amp section bypasses the cab when connected, there won't be any way for the amp to generate feedback, as this is created between the sounding speaker of the cabinet and the guitar itself, so you'll have a closed(soundless) loop from
guitar > amp > interface/whatever
This is why when you see rockstars getting the feedback sound, they tend to stand right in front of their amps.
If you want the feedback sound, you'll have to invest in a microphone and place it in front of the amp, connect it to the interface and record that way. You'll get a more natural tone through the cabinet, as the line out is generally meant to be connected to another cab, it doesn't sound all that great recorded raw (of course this is open to subjective opinion), and microphone placement is very important.
Otherwise, if you can record the cabinet and line out simultaneously, you'll get the feedback through the line out, but it might not sound all that great.