We bought them at the gondola station in Zermatt. It was 103 CHF to go up to the top. I didn't bother booking them online because we hadn't decided what to do until we got to Zermatt.

In June most cable cars are running. They generally have maintenance in September/October. Trockner Steg was open when I went in June but only for drink and cake. It may be the same this year but I don’t know. Assuming all the snow has melted then the walk to Schwarzee is open. Check the weather before you go as if there is a strong wind then the gondola may not be running but it should be. Of course you can still walk down from Schwarzee by one of the two routes to Furi. The gondola is always running from Furi to Zermatt.

Hello! Thank you for your interest. Whit the ticket Zermatt-Matterhorn glacier paradise you travel (during the normal timetable) from Zermatt via Furi - Schwarzsee and Trockener Steg to Matterhorn glacier paradise. We are looking forward to your visit, sunny greetings

Doubt boots are necessary though closed shoes for sure and warm clothing. We took the cable ride from Zermatt and it was amazing. Coming from Cervinia, Italy by road is @8 hours one way. Winter may be skiable though unsure about tours since we were there in summer and the only way was via road.

　私は2019年6月にミラノからツェルマットに入り、2泊した後氷河急行でチューリッヒに行き1泊というスイス3泊4日の旅程でした。 　２泊３日のツェルマットですが到着は夜の7時過ぎ、そして出発は朝一番の氷河急行と言うことで実質1日のみの滞在でした。１日しかなかったのでピークパスを使い、ゴルナーグラートを早朝と最終の夕方の２回、マッターホルングレッシャーパラダイスとスネガにも行きました。ピークパスは気にせずどんどん乗れるので楽でした。 　チケットの買い方はスイスの滞在日数と山岳鉄道に乗る日数、そして過ごし方によると思います。金額は季節によって変わるので要注意ですね。 　ハイキング主体で限られたルートしかゴンドラや鉄道に乗らないのであれば、片道チケットでもいいのかもしれません。ただ素敵な場所なので予定以上にまわりたくなったり、天気の関係で運行中止など予定が変わることは考慮されたほうが良いと思います。