Yes, I think that is a key issue with EU Freedom of Movement. It does sound positive if the EU is thinking about a language requirement.
I think the problem with FoM as set up by the EU was that it became all about rights, with no sense of corresponding responsibilities. To my mind, if I chose to emigrate to another country, it seems obvious that should come with a responsibility on my part to learn the local language, and to familiarize myself with that country's law, customs, way of life, etc. as a minimum so that I don't for example end up acting in ways that would be normal in the UK, but would come across as offensive or threatening to most people in that country. To me it therefore seems perfectly reasonable that any country should be able to impose requirements on would-be immigrants to do likewise, but EU FoM rules - as far as I can make out - prevented that.
I think I'd also feel some responsibility to attempt to integrate with the local communities and to seek to contribute to life there - and not end up forming part of a 'British' ghetto in that country. That kind of thing is much harder to regulate because it's very much in the realm of, personal lifestyle choices; but even so, it does seem to me concerning that EU FoM rules make no acknowledgement of that as an important part of migration.
Let me preface this by saying that I'm a huge supporter of the EU, but:
Yes, I think the big issue is that the EU leadership never imagined the kind of mass population movements that took place post-2004. It seems to me that the EU12 (and subsequently EU15) thought that it would progress on the same way that it had been prior to Schengen and the Customs Union, where people would take jobs in border areas, but nothing more. You can see how it evolved in the 1980s in Strasbourg/Kehl, where the two cities have effectively merged by now. That meant very little controls on FoM, and when it became clear in 2005-6 that FoM was resulting in significant problems, the A8 (subsequently A11) group of countries were strong enough to resist any controls on FoM. I remember the Brexit referendum as seen from the Polish perspective, and it was absolutely clear that the Polish government was not going to agree to any concessions on limiting FoM.
There was some degree of warning in how the Brits formed enclaves in Spain, and how the UK criminal element found refuge in Spain. Yet, it seems that it wasn't taken seriously, probably because the Brits themselves didn't really use things like schools there. I was chatting with one pub owner in February, and he reckoned that out of all his mates, only 10% at most could speak passable Spanish.
With regards to limits: yes, in hindsight, I suspect the EU15 would have imposed limits before the 2004/7/13 accessions if they knew what was going to happen. The lack of limits have caused a demographic disaster in parts of the EU, such as in Eastern Poland, and there are sociological consequences that are being largely ignored in the pursuit of FoM. For instance, what happened in Eastern Poland: children left with grandparents while the parents worked abroad, or one parent being mostly absent for years so that they could build a big house in the countryside. The effects of this will be felt for generations, and that's before we even discuss the major brain drain that took place in the A11 countries.
The question is: how do you limit people? One option could have been to require A11 workers to get a work permit, and only to issue the work permit if the proposed place of residence could accommodate them. But that would require a huge amount of data and investment, and even then, I'm really not sure how feasible it would be in practice. Another option would be to simply impose a hard limit, but at the same time, the UK (and others) quite happily found places for them to work. Maybe one possible option would have been to impose a 'migration tax' to expand public services, but then again: they already pay the same tax anyway.
I thus think whatever government we have in the future needs to work towards a compromise position who will make some consideration, at least, of the views of those of us who want a closer relationship with continental Europe.
I think that once the Johnson era (and I'd include Truss in this) is consigned to history, we'll see a quick agreement with the EU on a wide range of things. I could even see limited FoM returning for workers in exchange for financial passporting rights.
As long as it's really serious crimes. I would hope that migrants would not be deported for, say, speeding, or other minor crimes of a similar nature.
I think this was and is one of the major problems with FoM: it allows convicted criminals to simply move abroad. It should have been clear from 2004 onwards that anyone convicted of a serious crime (let's say one where they were imprisoned for the sake of argument) would have to obtain a visa/residence permit and that FoM wouldn't be in place for them. But again, this would have required a system where it could be monitored, and that would be quite difficult without abandoning Schengen.
I don't think there are really any easy answers, and some of the UK concerns were valid (such as not being able to block known criminals from entering). The UK did need a brake by the time that the EU referendum came around, and had Cameron been given the right to limit migration and benefits for 4-5 years, Remain probably would have won.
(on the benefits topic: I always thought that benefits should have been capped at the 'home' country level. It was clearly a very sore point for many Leave voters...)
) were very, very quick to use as much of the infrastructure as they could. Poles, for instance, are hypochondriacs, and they are used to running to the doctor over very minor things. If you've got a Polish mother with two kids, then she will be reaching for the doctor every time the children have a sniffle, whereas our culture is much more suck-it-up-and-get-on-with-it. 
