Mode confusion

If a Cmajor scale is composed of C D E F G A B,
and i want to play the Dorian mode in C. it will be D E F G A B C right? which i need to start on the Second Degree of the scale.

Almost - it'll be D E F G A B C D (D Dorian)
but i saw a video which says the formula of a Dorian mode is 1 2 3b 4 5 6 7b,
which is C D Eb F G A Bb right?.

No, but I think what's gone wrong is you're forgetting to adjust your starting point - The person on the video is relating that formula to the Major scale - which (sticking with D) will give you D E F# G A B C# D. Compare that to D Dorian above.

Because you need F and C naturals, not sharps, you have to flatten the F# (the 3rd of the Major scale) to get F and flatten the C# (the 7th) to get C.

And what you've done by thinking C D Eb F G A Bb C is take it back to a scale based on C instead of D. This -> C D Eb F G A Bb C - is in fact C Dorian, a mode in the key of Bb.

And what you've done by thinking C D Eb F G A Bb C is take it back to a scale based on C instead of D. This -> C D Eb F G A Bb C - is in fact C Dorian, a mode in the key of Bb.

oh i think i get it now, if im playing "G Myxolidian", im on the key of C righhht?.

Another question is. What if i want to construct a triad from "G Myxolidian" G A B C D E F G, i will took 1 3 5 which is G B D righT?. and if il start my solo over that triad and i will used "A" as a first note on my solo , does that mean im on Dorian? soloing over Myxolidian?

You get the same triads in all related modes. G would be the tonic triad in G mixolydian.

But don't confuse modes with harmony, or think that certain modes will only work with certain chords. Music is kind of a three-legged stool: rhythm, melody, and harmony... modes are melody tools, chords are harmony tools.

Both the melody and the harmony will have a "tonic" - that's the point where they feel at rest. In most cases, the two will be the same. But a melody doesn't have to start on the tonic; in fact, most interesting melodies don't. Example: if you play "Happy Birthday" in the key of C, your first note is G... but you are NOT in G mixolydian! So your choice of first note has nothing to do with what mode you're in.

Your choice of last note will probably indicate what mode you're in, provided that your melody sounds "complete" at that point.

Another question is. What if i want to construct a triad from "G Myxolidian" G A B C D E F G, i will took 1 3 5 which is G B D righT?. and if il start my solo over that triad and i will used "A" as a first note on my solo , does that mean im on Dorian? soloing over Myxolidian?

The triad of G, B and D is a chord of G major, and if you pick a first note of A it will sound dissonant, forming a major 2nd interval against both the G and the B in the G chord.

Keep on top of your keys and (as Noteboat mentioned) don't confuse scales/ modes with harmony:

The chord of G is one of the primary triads in the key of D, the dominant in the key of C, works in Em and Am, and is the tonic in the key of G.

G mixolydian (G, A, B, C, D, E, F, G) is a scale-based mode in the key of C.

A dorian (A, B, C, D, E, F#, G, A) is a scale-based mode in the key of G

So if you play (your example) a triad of G-B-D -> you're playing a chord of G and you could be in any one of a number of keys; but you're not playing G mixolydian because that's a mode of a scale.