LB – the term could probably be used either way. It would depend on the context of the statement/discusion.
However, it usually means that both (or all) opinions are legitimate, especially if it’s a halachic issue. If someone asks, “what is the halacha regarding…”, and the response is that it’s a machlokes, that would generally mean that both (or all) opinions are legitimate.
An exception might be if the person says that it’s a machlokes if it’s a or b but it was decided that the halacha is b.
I believe that the mezuza issue that you quoted falls in this last category. It was a machlokes, but a decision was made, and according to halacha, we now have to follow that decision (at least I think so – I don’t know enough about the halachos of Mezuza to say for sure.)
If you are talking about a machlokes Rishonim, you would have to find out what the Achronim and contemporary Poskim say. You can’t just decide to follow a particular Rishon. The same goes with a machlokes Tanaim or Amoraim.
If the machlokes is amongst contemporary Poskim, there is some room to say that you might be okay whoever you follow, but it is not so simple.
First, you have to verify that the Poskim you are talking about are all accepted legitimate Poskim. Then, if you are Ashkenazi, you have to make sure that they are Ashkenazi and if you are Sephardi, you have to make sure that they are Sephardi.
Aside from that, it can be problematic to go by one Posek for one thing and another Posek for another thing. For one thing, there may be an inherent contradiction between the two psaks, and that is something that you wouldn’t even necessarily know. However, it is less likely for this to happen if the two psakim are in different areas of halacha (for example, one has to do with hilchos brachos and one has to do with hilchos Shabbos).
The other problem is that you’re not supposed to always be looking for the easiest opinion to follow, and to each time choose which opinion to follow based on the fact that it’s easiest. It’s not a particularly intellectually honest or Yarei Shamayimdik approach as a general rule.
On the other hand, as someone who is in the process of becoming Frum, there could be much more room to say that it is okay to do something as long as there is some legitimate opinion. Especially in an area that is difficult for you. You certainly should not be looking to make things harder for yourself than necessary.
As a general rule, the best thing to do is to have one Rav and always go by him. But that is not realistic for everyone (especially for women) and I’m not sure that you are even in a position at this point to be able to figure out who you should be choosing as a Rav. And the danger exists that you may choose someone whom you shouldn’t be choosing.
So, probably what you should do when it comes to basic halacha is to read through the mainstream english books that have been written on specific topics. You should probably choose one book for each topic. Try to make sure it’s a mainstream sefer (neither too left-wing nor too right-wing) and that it is well researched and well written.
For Hilchos Brachos, I would recommend Rabbi Bodner’s sefer. For Hilchos Shabbos, I would recommend either Shmiras Shabbos k’hilchasa, Rabbi Ribiat’s sefer or Rav Eider’s sefer.
Rav Eider’s sefer is very well-written, but the downside is that I don’t think he ever wrote/published all of the melachos. Also, he presents a wide range of opinions which may confuse you. I never read Rabbi Ribiat’s sefer but it looks very thorough. It might be too thorough for you though – it is a lot of volumes and it would take a long time to go through it.
So Shemiras Shabbos k’hilchasa might be the best option for you. It will give you the basic practical halachos according to a mainstream poseik.
There also may be online or telephone shiurim you can listen to, but I’m not sure what’s out there. And of course, there may be shiurim in your neighborhood, which it sounds like is something you do a lot of.