Is ascended gear worth the effort?

You're in the position that I was in before I went to crafting ascended gear. Simply ascended weaponry gives a very noticeable boost. The stat boosts are decent, remember to include the infusion in your math. If dual-wielding, you'll find your main hand weapon is likely worth the most, as those skills more often tend to do damage and there are three of them. If two-handed, even better. If you're looking for so-very-obvious efficacy-to-cost ratio, ascended weapons will do it. Note: I was lucky: axe/dagger means only one craft to get each. I would not go through all that again just to upgrade my staff. You may be running two weapons of different crafts, and that will bite. (or you are luckily using a two-hander)

Ascended armor is nice, but for the cost in gold, at least as far as light armor goes, run the math before you make a decision. My pants stand to cost my light-armor about 75-85g alone for a boost that is not much compared to either of my weapons. As of this writing, a Bolt of Damask is going for 12.5g on buy order.

Ultimately, a fully ascended character vs. fully exotic character (no asc. trinkets) is the difference of night and day for min/maxers. I asked myself what else I would do with the gold, if I really didn't want ascended armor? A furniture tonic and fused skin - the former 50g and the latter 225g for a single skin. Stat boosts win out for me, but perhaps they do not for you. I got the furniture tonic, love it, and am now working my way to full ascended armor.

Should I now get an ascended armor and weapons?
If you want to.

Or is there any other way to improve my character from now on by any other action?
No. Improving your actual stats will require ascended gear.

Is there a less costly (time- and gold-wise) method of improving my character further?
No.

Are there any other steps, which can be taken aside from getting more ascended gear to improve my char?
No.

Would for example leveling professions like chief and artificer, to get potions and food be more useful to boost my stats?
Mastering a crafting profession has no impact on your characters stats.

Is crafting ascended armor (and weapons) worth the effort to improve my char
I don't think so, but that's just my opinion.

Should I now get an ascended armor and weapons?
At this point and time, it s about wether you want to sink more Time/Gold into the game it took me a month to finish weapon smithing and at this this half a month to get armor smithing to 400. the total cost of getting trinket can be timly.about a month between Fractals,WvW,and Dailies

Would for example leveling professions like chief and artificer, to get potions and food be more useful to boost my stats? Is this more time-intensive than a ascended gear (to gather resources, craft them), if I want to have a steady supply of those consumables? Why not both since both would be advantageous to have. but in the long run Acended gear would pay for its self

the only other stats proggesion after this is get max AR on each piece

and if you want more research on the benifit and dept of stats progession, here is a nifty video on what it looks like with balls to the walls max stats