what to plant to get some privacy?

Both privet and forsythia are quite effective but are unlikely to be good in this situation.. The lack of direct overhead light will create problems.

Forsythia, in particular, won't be happy. It will continually try to lean outwards to the light. This will require regular trimming and, therefore, loss of flower bearing branches.

 

Yes, once the get established. This is a good time of year to do it. Dig a reasonable sized hole, put in some good compost, plant and water regularly. They need the water in order to settle in. Winter time it tends to be wetter and therefore easier to look after, but remember that the existing conifers will be sheltering the ground and keeping it dryer.

 

'Minima' is exactly what it says - minimal. That's a dwarf variety and no good for you.

I don't think your trees are Chamaecyparis. They look more like Leylandii. They're much cheaper to buy, grow quite quickly and are OK to control if you keep them cut regularly.

Never cut back past the green part of the leaves. If you cut back into the brown part they won't regrow.

 

The Jackson one that you've posted is not the same colour as those already growing. It is a slightly golden colour and grows slower, but thicker than the Wyevale one. I'd go for the Wyevale one.