They have well-developed public transportation system. Tickets can be purchased in ticketing machine or counter. I would say the price is relatively similar with Western Europe. I took a station from the airport and it costs me 3€.
Ben Gurion airport to Tel Aviv city center only takes 15 minutes
There are bus service from Tel Aviv to Jerusalem, which costs 4€ for single trip. If you took bus in Tel Aviv Central Station, there are 7 floors in total. The 403 direct bus to Jerusalem is located on 6/F, Platform 6 or 7.
Moovit is commonly used by the locals for checking the public transportation way. Google map here is not so accurate.
Sabbath is Judaism's day of rest and seventh day of the week. According to halakha (Jewish religious law), Shabbat is observed from a few minutes before sunset on Friday evening until the appearance of three stars in the sky on Saturday night. Shabbat is ushered in by lighting candles and reciting a blessing.
Shabbat observance entails refraining from work activities, often with great rigor, and engaging in restful activities to honor the day. Basically all the shops are closed but still there are convenient stores, Muslim stores available. The key issue would be public transportation. Public transportation is not available in this period. It's better to stay near the city center, like Old City in Jerusalem, rent a car and book a tour at less 2 days before Shabbat. It would be quite inconvenient if you are doing inter-city travel with public transport.
You may be curious about the dressing of people with different religions and even the soldiers, but try not to take photography of them because some of them are not allowed to show their faces in their pictures. Even though for kids, it's better to ask for their permission before taking photos. Same with some buildings, their architecture look like tourist attraction. However, some of them are residential area or private place. Be respectful and polite all the time.
People here can speak English in general. But if you are looking for directions, it's better to find your own way than asking the locals. WiFi is available anywhere in city center. But I bought a SIM card when I decided to visit Jerusalem alone for 2 days, the minimum usage is 10GB and costs 20€. Even though I traveled for four days, they have limited choices for tourists sim card. If you have any local friends here, you may ask them to give you their SIM cards under their accounts, usually they have 10 GB for 6€ per month. in airport. I bought in central bus station and costs me 15€.
The average price per night in Tel Aviv is 30€ per night while the price is dropped when I visited Jerusalem, which is around 10€ after Trump . There are extensive network community of couchsurfing here so you can have a try on it. But be aware of the background of your host if you are a female solo traveler. It is important not to find a host in a hurry.
I would say the price here are similar with Germany or the UK. It costs around 8-10€ per meal for some local food. Surprisingly my Finnish friends said some of the Finnish wines sold here are more expensive than in Finland.