I have a problem with maintaining an straight tempo
when I have to use the following rhythmical patterns
Even when I start the computer to play something like that
straight and without mistake, I feel something is grinding…
How to deal with this???
I’m not an expert but I think that a sensible advice would be to:
You may also want to get comfortable with each of the tuplets before you start combining them. And then play each one of them for shorter and shorter periods. Example: let’s say you are kind of comfortable with them separately. Now play 7-tuplet ~4 times and only then switch to the 6-tuplet. Once you get better at it, play each 3 times, then twice, and then play the example you provided as it is written.
Once I had in interesting exercise: I would make cards with different tuplets going from quarter note to 10-tuplet and shuffle it. Then I would put the cards in a line, set metronome to 40bpm, and try to play whatever rhythm cards instruct. If you try it, there’s a risk you’ll end up in [Arkham] asylum. I take no responsibility 
Most counting systems are based on one syllable per one hit.
Here’s a couple ways you can tackle the thing:
Numbers Only
1 2 3 4 5 6 7
Say every number except seven (two syllables), you can change it to sen, if you’re not using English the principle of one syllable per hit remains
Mike Mangini’s Way
“1 and 2 and 3 and 4” for 7 and “1 and 2 and 3 and” for 6
Konnakol (more to find on Youtube)
Ta Ka Di Mi, Ta Ki Ta = 7 (4 + 3) and Ta Ki Ta, Ta Ki Ta = 6 (3+3)
Also, the faster the tempo, the more of a feel these tuplets have to become, while even numbers have “a middle”, odds do not so you kinda have to get an even deeper feel for them, as in not just counting, at lower tempos for them to become usable at higher ones, specially if you’re improvising.
I use a similar system. I modified it because sometimes it doesn’t make any sense to me. Example is the sextuplet that you wrote: Ta Ki Ta, Ta Ki Ta. The “Ta” gets repeated way too many times for my preference and it’s hard to pronounce those two “Ta” in a row. My tongue isn’t trained enough for that stuff That’s why I pronounce rhythms that are divisible by three as Ta Pee Ka 
I can say that again and again without any repeating syllables and all three sounds are produced with different parts of mouth.
Thanks 
I didn’t know that he counts like that.
Where things are generated on a computer and/or paper, feel may not be involved. That said, usually deviations from the underlying rhythm borrow from other constant threads of rhythm in parallel.
Besides getting super familiar with each of the rhythmic threads in the music and combining them, I concur with the others in looking to vocalization to help with that.
Be it tabla bols or Ed Friedlands vocalizations in Bass Grooves, there’s obviously a lot of value in the verbalization practice.
Thanks for all answers but I see some mistake/inaccuracy
Mike Mangini’s Way
“1 and 2 and 3 and 4” for 7 and “1 and 2 and 3 and” for 6
this is ok when we play in one tempo like here
https://zapodaj.net/images/ba5f4b21fa8f6.png
but in this case the speed of the individual notes it changes
https://zapodaj.net/images/29e7937fedabe.png
so it’s not about counting individual notes
but about how to play at one tempo
in different rhythmical sections in one measure 
Can’t speak for the others, but that’s the issue I thought I was speaking to.
Have you ever worked through the Warne Marsh meter studies?
I came across them in John Klopotowski’s book “A Jazz Life” about Warne Marsh and having lessons with him, I don’t know if it’s something that’s kicking about the internet somewhere or other.
Basically it’s just about playing all the different subdivisions until you can play any meter over/in/with any other.
edit: https://www.johnklopotowski.com/book-preview#meterstudies
there’s a preview