MumTryingHerBest said: "Is there a valid reason why they have to convert?"
Any maintained school can apply to convert, using this process. They don't have to convert, although anecdotally some schools have felt under pressure to do so in order to avoid the Sponsored Academy process, or in order to have certainty over their future funding.
"I am somewhat confused as to how the approval of a Free School is based on there being no surplus school places in the area, when the application process only requires them to demonstrate a certain level of interest."
Because as part of the approval process the DfE looks at the local context. They monitor shortages, and will contact the LA to discuss the impact of a new school.
The demonstration of support is the responsibility of the group behind the proposed school - they need to show that their school will be popular with local families because, for the reasons ooutlined to NLondonDad above, there is no point in creating an unpopular new school, even if new places are needed. (Local Authorities have sometimes made that mistake in the past - their new schools were no more guaranteed to be popular than Free Schools, but their consultation processes didn't need to prove that they would be popular, and sometimes didn't get many responses at all).
"If an area has a projected shortfall and a Free School application is approved, land procured and building comences, will it really be prevented from opening if there are still school places available in the area at the time of opening? Does this not mean that there will be a lot of time and expense wasted in setting up of these schools?"
No, not if they're that far on in the process, with land procured and work commencing. Provided they pass all their pre-opening tests (Governors/Staff appointed, Ofsted inspection passed etc) I'd expect them to be allowed to open (but see answer to final question below).
Schools that have been deferred/cancelled in their pre-opening year generally haven't had enormous amounts spent on them. A lot of the work carried out by free-school trusts is pro-bono (i.e. they are working for free, just like LA school governors), and procurement of equipment doesn't begin until after the site is secured.
"the existing Free School I have referred to is schedule to relocate to a permanent site in 2016 (as mentioned on their web site)"
But has the permanent site been secured? If it is secured, but they just haven't announced the location, then that is ok. If they haven't secured anywhere yet then it is more of a worry. (Although in some cases I expect there are back-up plans that aren't in the public domain).
"Would the new Free School really be prevented from opening ..?"
There are no hard and fast rules - just lots of uncertainty (which is what is so frustrating for free school groups and parents supporting them). If it is politically expedient for the school to open, and it can be justified financially, then it will open, but those are two big "ifs" and there is no sure fire way of knowing in advance, especially as the unwritten rules are changing all the time due to public pressure, inter-departmental pressure etc.