Climbers advice

Hi Folks
just getting back into gardening after a year or so of not being able to do much - i'd like to get this trellis looking nice - the honeysuckle has survived but gone a bit top heavy - can i train it to go sideways to fill up the trellis either side?
also i have just bought an Ena Harkness rose intended for the right hand side - but its a bit shady that side due to the fence -[photos area facing south east ish] will that be ok?
also now i look closely at the rose [ i bought unseen click and collect!] it has what your very helpful site tells me is mildew on some of the leaves - i have sprayed with milk/water as advised - should i still plant it?
many thanks for any words of wisdom
Geoff