About svasaṃvedana (reflexive awareness) and having bodhicitta What is your view regarding svasaṃvedana? Do you accept or deny (the
existence of) svasaṃvedana?
https://en.wikipedia.org/wiki/Svasaṃvedana
https://encyclopediaofbuddhism.org/wiki/Svasaṃvedana

Can a Buddhist know whether or not he/she have really genuine and
firm bodhicitta by him-/her- self? If yes, then how? (Does this
question have to do with svasaṃvedana?)
I hold the Prasangika Madhyamaka as the highest and definitive of the Buddhist tenet systems. The prasangika refute the notion of inherently existing reflexive self-awareness. Here you can see Chandrakirti refuting the notion of Svasaṃvedana or rangrig of the Cittamatran school:

The above is taken from a commentary on Chandrakirti's Madhyamakavatara by Dzongsar Jamyang Khyentse Rinpoche. Rinpoche is a highly accomplished master of the Rime movement and has studied under all major schools of Tibetan Buddhism. It should also be noted that he is quite sympathetic to the Cittamatran school:

I won't highlight the actual rebuttal arguments that Chandrakirti invokes as you can click on the link above and read them and draw your own conclusions whether they are strong arguments or not. However, this is the conclusion that Chandrakirti draws:

As for your second question... Yes, it is possible to be aware of your own genuine realization of Bodhicitta. However, most ordinary people fool themselves into believing overinflated self-conceptions of their own achievements. Regardless, this self-awareness - whether mistaken or unmistaken - is only conventionally true and does not have one iota of true existence. That's because nothing whatsoever has one iota of true existence.

PS: If you would like to verify with another commentary on the Madhyamakavatara you can look at Ju Mipham's commentary here. If you do you'll find that it is in complete accord with the above.