Can you pray to gods like Indra, Agni, Varuna without doing a yajña? Just praying to them in mind, chanting mantras in mind or saying prayers in mind in languages other than sanskrit.
Is it possible?
Yes, definitely. For example, there's a stotram for the Ashvini Kumaras (considered to be 'Vedic' 'Gods' by most), in the Mahabharata Paushya Parva in the Adi Parva. It's the 3rd Adhyaaya and starts from the 56th Shloka in the Kumbhaghonam edition.
If you extend that same reasoning a bit, there's no reason you cannot pray to Indra or Varuna.
There are relatively newer age things like Indra or Agni Sahasranaama Stotrams as well which you can access at sanskritdocuments.org after a bit of searching.
As for other languages, there's a history of that from TulasiDaasa for example. As well as many others. Don't worry, Devataas aren't that ignorant that they will be limited by the language you're using.
As for mental prayers, those only apply to Devatas who have access to your mind (otherwise the prayer won't reach them). It's not really much to consider, the vast majority of entities you'll ever come across do have such access.
Try to do it in the day time, though.