Is it aloud to make the duaa made in various timings (like after salat and other times both with raised hands and without) non verbally i.e. formulating the wished dua (or the authentic duaas from quran and hadith) in ones hearth and saying it in mind and not saying it with tongue.And is this also aloud inside salah (like reading the duaas in tashahhud, sajdah etc)
You cannot make dua only in your heart if the dua is prescribed as being stated by the tongue, such as those inside the prayer. They must be loud enough to hear yourself (under normal circumstances of noise and hearing ability). However, if you just want to ask Allah for something, as it occurs to you, you can to this in the heart alone.