Hi Ziv -
Wlcome to My Swiss Alps. Sounds like a great trip.
Good thing you have booked already...that is a busy time in the Alps.
For some of your general questions, check these links:
No one can predict the weather in any detail in the Alps more than about 24-48 hours ahead of time. You'll have enough time there to allow for a couple of days with poor visibility.
This is one of the better weather forecasting sites:
www.meteocentrale.ch/e n/europe/switzerland/w eather-wengen/details/N-3517887/
If it is sunny, you'll need at most a light jacket on the trails. But, I always carry rain gear.
This site may help with averages and expectations::
A couple of specific comments:
Do you plan to climb from Wengen to Kleine Scheidegg, then Männlichen?
This map will help you with altitudes:
map.geo.admin.ch/?topic=ech&lang=en&bgLa yer=ch.swisstopo.pixel karte-farbe&layers=ch.bav.ha ltestellen-oev,ch.swisstopo.swiss tlm3d-wanderwege&layers_visi bility=false,true&E=26 35809.36&N=1161941.29& zoom=5
I've turned on "Hiking Trails."
It is almost universally recommended to walk from Männlichen to Kleine Scheidegg.
Apart from the fact that it is slightly downhill, there is a substantial psychological effect from seeing and feeling the Eiger grow over you as you approach it.
I'd make a special effort to hike it in that direction.
You could take a cableway to Männlichen walk to Kleine Scheidegg and then do the walk you propose from KS to AlpiIglen via station Eigergletscher.
Lauterbrunnen to Stechelberg and return will only take half a day, even if you stop to see the falls along the way:
You'll have time for Mürren.
Schynige Platte to First is far from an easy walk.
About 800 meters climb up to Faulhorn.....at 2681 meters.
www.myswissalps.com/fo rum/topic/traveling-alone-in-bernese-alps-in-july?actionMode=editPost&po stId=615f6786-d6a0-6af6-92ea-ff000057114d&redirect= true#reply
Are you used to high altitude hiking? There is some pretty serious climbing at high altitude.
Acclimated to the heights and the "thinner" air? And, the last cable car down from First is at 1830.