I've run into Houdini, and couldn't get any easy way of making fluids, hair, or cloth.
As familiar with Maya paint fx, I hoped I'll find something like it. Still haven't looked into Lsystems though.

Is it necessary to build own tools in order to have these effects, or some pre-built assets can be found?

And again, even if I achieve such effects, would it be possible to output them also to Renderman or Mental Ray (I used to always restrict myself when working with Maya and MR PRMan due to known incompatibilities)?

You can create Cloth and other sims for things like guide hairs using DOPs in Houdini 8, but the general opinion from the embattled veterans seems to be that these features won't really be usable until version 9. I've managed to make some nice things with the current cloth in 8, but it deffinitely can be difficult to work with. Syflex is available for Houdini, but a word if warning, the last version of Syflex I used was quite anti-Houdini in it's workflow. I don't know if it's improved in later releases or if or how well it is supported.

To render hair, you have many options, the best probably being to write a hair DSO, but you can search odforce.net forums and find all sorts of useful ideas and tools.

Fluid sims may eventually show up in Houdini itself, but there are third party options available like Real Flow from Next Limit, and Hydrous Tools from Martian labs. Depending on what you are after, you can make some nice looking fluids in Houdini with the currently availble tools and some clever thinking. Play with geometry shaders, displacement shaders, particles and metaballs. There's also a freely available Houdini Ocean Toolkit floating around here and on Odforce.

For plants, you won't find anything like PaintFX in Houdini. I recently had my first go at making a really high res hedge with LSystems in Houdini and I think the results are pretty impressive. It took about a solid day and a half of wrapping my head around the syntax used to create LSystems, and another couple solid days of work, but the results you can get out of LSystems for both low and high res plants with the help of scattering and the copy SOP is pretty incredible.

As far as rendering with PRMan or Mental Ray… First you must make sure you have the proper rendering license. It can't be done in Apprentice. You'd need Master or a Render Plus license for that. If you have the license, you'll need to set up the environment properly. The renderers and their shaders need to be in your path and have their environments otherwise set up properly, and Houdini will need to know where the shaders are. You'll need to check the docs or ask more specific questions about this because it's a lot to explain here.

Thanks MichaelC, for the attention.

I see the point:
I hoped that Houdini might have all stuff integrated, like in other 3d apps, so that one doesn't have to bother looking for more and more expensive plugins. So it seems, only with huge knowledge should one approach to Houdini in order to achieve more.

Houdini doesn't really have any canned solutions for anything, and probably never will. I'd go as far as to say that even things like the shaders in Houdini aren't really meant to be used as is, they are just provided for convenience. The main thrust behind Houdini's development seems to be to provide small general purpose tools that are intended to be used to construct larger solutions. It means there's more initial work to getting things done than in any other software but the nice thing is that once you do have a solution you can easily reuse, repurpose and extend it. So in the case of something like hair, you aren't going to find hair tools specificly, but things you can use to build a hair solution.