There's a "yes but" on the last one.
The UK does not have the ability to restrict worker immigration from other EU28 states, except in a limited, short-term capacity. It can - but didn't - impose a restriction on workers from "new" states for a period of up to seven years after the new state has joined. For example, Austria and Switzerland have imposed this restriction on Croatia, which joined in 2017.
In addition, should an EU28 immigrant to the UK not be economically active within three months, we can remove them to their home country. Only we don't register them, unlike some other EU nations, so we can't.
As we neither imposed the travel restrictions on Poland when it joined nor registered its migrants, we got the media trope of Polish itinerant workers coming over here and taking our plumbing jobs, and taking the money back home to Poland. This stokes fears that should Turkey join, we'll have to accept Turkish workers - and we will have to, no later than seven years after Turkey joins. The problem with Turkey is the fear that much of its migrant population would be Syrian refugees who are, according to the Daily Mail, Da'esh terrorists because they're Syrian...
... and whether that's true or not, it does raise questions about exactly how safe and secure total freedom of movement across the EU actually is. Turkey's membership would give the whole of the EU a land border with Iran, Iraq, Georgia and Syria, meaning that anyone who could get into Turkey could travel anywhere in the EU without ever being checked. The UK's border agency is thus the Turkish border agency - we'd be entrusting our security to them (and the guys at the Eurotunnel in Coquelles).
This is a prospect that would be concerning for many - enough to vote to leave.