Help with hiking Jungfrau region/Zermatt 6-13 June

Hiking is my aims of trip to Jungfrau region and Zermatt, but I just noticed that hiking trails may not be ready, and some of the lifts are closed in early June.

I'm interested in these hiking trails:

1. Männlichen - Kleine Scheidegg - Wengernalp

If Männlichen to Kleine Scheidegg is not available, I would like to try Royal Walk. Did anyone try the Royal walk? Is it easy?

2. Grütschalp - Allmendhubel – Mürren (mountain view trail)

I just know Funicular Mürren - Allmendhubel is still closed when I'll be there, so I plan Grütschalp – Winteregg – Mürren. Are they much different? I want to go Allmendhubel because of the flower trail, Is it possible if I hike Grütschalp to Allmendhubel and to Mürren?

3. First -> Lake Bachalpsee

I'm not sure if the lake is still frozen, seems it's not worth to go if it is frozen? I prepared other alternatives like Lauterbrunnen to Stechelberg, or Schynige Platte, any other suggestion?

4. I'm very interested in 5-Seenweg (Five Lakes Walk) in Zermatt, I planned to start from Blauherd and then to Sunnegga. But only lift from Zermatt to Sunnegga will be opened, Sunnegga to Blauherd is still closed. Is it difficult to start from Sunnegga? If 5-Seenweg is not possible in early June, anyone can suggest another option?

Thanks in advance.

1- When the snow is gone,( I think) the Mannlichen . Kleine Scheidegg > Wengernalp trail is very easy and nice view on the Mountains and Grindelwald, Grosse Scheidegg.

The Royal Walk is also very easy, walking time about 45 minutes to the top and also back to Mannlichen.

When you are early on Mannlichen, you can do both on one day.

www.maennlichen.ch/en/ hiking.html

2- Grutsalp to Mürren is also very easy and you don'tgo op or down. Walking time about 1 hour. Allmendhubel is more higher then Mürren, you can walk from Mürren to Allmendhubel., so you can walk Grutsalp>Winteregg>Mürren>Almendhubel, but also Grutsalp to Almendhubbel is possible.

3 - First to Bachalpsee is a nice hiking. I think the see is not frozen in June. Forget not the new "First Cliff walk" on First, near the restaurant. You can also walk: First>Bachalpsee>Bort, about 2 or 3 hours.