Can I make out/go down on a guy once I get permanent retainers like photo attached? (Photo)

Permanent bonded retainers should not be an issue for the activities you describe.  When the retainers are placed they should feel smooth to your tongue. No one will know its there. 

in case of retainers, it depends of type of mal-occlusion [pre treatment condition]. for eg. in case of anterior generalized spacing, bonded permanent retainer is indicated. In lower arch bonded retainer is good option because other retainers are removable. so you have to remove that every time before having anything. you do not want bonded retainer thn you can go with essix retainer [ removable and invisible] . but as i told you, ask your orthodontist about  tre treatment condition and ideal retainer type for that.

The wires used in these type of retainers are very small and the adhesive material used to hold the wire in place is the same material used to repair a broken tooth, meaning it is very strong and can be polished very smooth.  The strength means the little bumps of adhesive are very small and very smooth so they are barley noticed by the patient.  It would be difficult for another person to be able to detect them with any other appendage than a finger...
Furthermore, the back of the teeth are actually perpendicular to the orientation of the tongue and throat. Patients find that it is actually a bit difficult to get a tooth brush up against that side of the teeth to get them clean.  Anything larger than a tooth brush would be impossible to get anywhere near the wire. 
I would also humbly suggest that this type of retainer would be a superior choice in your case since these types of activities create additional forces that will make your teeth more likely to move out of alignment.