How does the comparison of rates depend on mutual speed? If I'm moving with a considerable fraction of speed of light, the time and any process in my system will be going slower. If B is an outstanding person that is watching me passing by, he will see everything in my system in slow motion. This means he observes less ticks per seconds; thus the ticks are slower or the interval between the ticks is bigger. From my perspective everything is normal and time is not running slower. 
Is it okay to talk about the speed of time in this context? Is it okay to say: "The shorter the interval between two ticks the faster the speed of time."?
 A: When one compares the spacetime coordinates between own rest frame and some other inertial frame, the time coordinate is transformed as such:
$$ t = \frac{\tau}{\sqrt{1-\frac{v^2}{c^2}}} $$
where $\tau$ is the proper time and $t$ is the time in some inertial frame. I think you can lazily but carefully refer to the following quantity as "the speed of time" in some frame with respect to your own rest frame:
$$ \frac{d t}{d \tau} = \frac{1}{\sqrt{1-\frac{v^2}{c^2}}} $$
Which is, of course a Lorentz factor of the boost.
A: 
If I'm moving with a considerable fraction of speed of light, the time and any process in my system will be going slower. 

That's an improper, careless, lazy description ("slower" -- in comparison to what??).

If B is an outstanding person that is watching me passing by, he will see everything in my system in slow motion.

Taken literally, that's not correct either.
Instead, the rate of what B (being stationary as a member of an inertial system) sees of you (or A), moving straight along B's line of sight ("${\text{LoS}}$") through B's system at speed $c~\beta_{\text{LoS}} = v_{\text{LoS}}$; towards B, right past B, and finally away from B, is related to your own (proper) rate by the Longitudinal Doppler factor which is derived to be $$\frac{f_B[~\text{observing }A~]}{f_{A\text{ (proper)}}} = \sqrt{\frac{1 - \beta_{\text{LoS}}}{1 + \beta_{\text{LoS}}}},$$
which is less than $1$, therefore corresponding to (mutually) "seeing slow motion", or (mutually) "red shifted", for $\beta_{\text{LoS}} > 0$ (i.e. in the course of A and B finally receding from each other);
but larger than $1$, therefore corresponding to (mutually) "seeing fast forward", or (mutually) "blueshifted", for $\beta_{\text{LoS}} < 0$ (i.e., by the suitable sign convention, in the course of A and B initially approaching from each other).
This is to be contrasted with the Transverse Doppler factor
$$\frac{f_B[~\text{projected from successive meetings with}A~]}{f_{A\text{ (proper)}}} = \sqrt{1 - \beta^2},$$
which characterizes (mutual) time dilation directly, as the Lorentz factor $\sqrt{1 - \beta^2}$, and where the members of B's inertial system infer the value of frequency $f_B[~\text{projected from successive meetings with}A~]$ by determinations of simultaneity between each other.

This means he [B] observes

... or rather, the members of B's system determine by simultaneity projection ...

less ticks [of A] per seconds

... than: A counted properly (him- or herself) likewise per seconds; provided that what A and what B separately and properly mean by "one second" are in fact equal durations. 
Of course, it can be measured, trial by trial, whether equality is the case, or whether there is any difference;
by first (separately) determining the value of the mutual speed parameter $\beta$, and then calculating and applying the appropriate factors described above to compare $f_{A\text{ (proper)}}$ and the corresponding $f_{B\text{ (proper)}}$.

Is it okay to talk about the speed of time in this context?

I consider such talk intolerable. (This is indeed only a statement of my opinon, which is however informed by didactic experience.) Instead, it is perfectly adequate and correct to consider and to speak of rates, as described above, which are of course understood to be proper.
