On your fourth point, historically our governments have mostly been majority governments but there is no reason why they have to be. Any TD can be put forward for Taoiseach, the Dáil (and only the Dáil) as a whole votes on them. They then nominate a cabinet to form a government. There are constitutional limits on the size of the government (7-15 members incl Taoiseach and Tánaiste). Note that that number doesn't include junior ministers and ministers of State.Traditionally the party leaders are nominated for Taoiseach (unless they have agreed to be a junior partner in a coalition).
Minority governments have occurred occasionally in the past (think of Alan Dukes Tallaght strategy to support a FF minority government in order to provide a stable government). FG or FF could form a minority government, in theory SF or Labour (now they have Willie Penrose) could do so to but practically they are far too small to do so alone. SF have declared they won't be party to any government they don't lead (ah the gentle sound of flip-flops as Gerry ambles over to his trampoline). Labour have given an absolute statement that they intend to go into opposition. As have the Lúdramán Left (well it is Seachtain na Gaeilge!)
FG/FF would be a majority government even though some idiot has decided that water charges should be a "red line" issue - which is simply preposterous - it is still more likely than any other coalition. It would provide the country with stability but it could come at a cost for FF in particular - not all FF TDs would be happy to go into coalition with FG and some may be willing to leave over the matter (O'Cuiv would be one to watch). Defections are possible but less likely with FG.
As FG and FF hold 94 seats between them, leaving 64 seats for other parties and independents, no coalition can have a majority without one or the other of them.
(Don't forget at some point someone will have to be Ceann Comhairle - they then will no longer be in the numbers game for government. Just before the Dáil rose, the government put through a change to ensure that the Ceann Comhairle can be anyone in the Dáil - up until now it has always been a member of the government party/parties)
The slimmest majority is 79. So FG would need to find 29 TDs to join them and FF would need 35. Labour and AAA-PBP have adamantly ruled out joining in, so that pool of 64 becomes 51. SF have notions so that 51 becomes 28. So even with the support of every independent TD, the Greens and the Social Democrats, such a government would not have a majority (and would have more factions than a Middle East war).
The most likely options are either a FG/FF coalition, a minority FG government. a minority FG + others coalition and the same two options with FF (less likely though).
If the Dáil can manage to elect a Taoiseach - we will have a government (possibly weak or ineffectual, possibly fragile but definitely there). That is the crunch point - getting a Taoiseach sorted.