Are showers available on the Everest Base Camp trek?
Yes, they are.
There are plenty of places where you can shower on the trek. The only issue with this is that sometimes the water isn’t hot. All of the showers available on the Everest Base Camp trek are heated by solar power so if it’s been a cloudy day or for a couple of days you're not going to get any hot water. Over the 12 days that we are in the mountains trekking on the Everest Base Camp trek, there are about four or five places that you can actually have hot showers if they are available. Some people do go hardcore and they only have a shower when they get back to Kathmandu. Having done this myself once in winter when there was no hot water, when you do have that shower it makes you feel like a million dollars after 12 days spent in the mountains but this isn't for everyone.
Most people on the trek and something that I highly recommend is to use wet wipes to have a freshen up in the mornings. This at least makes you feel a little cleaner if there isn't any hot water. There is always running water which can be used if needed but putting cold water onto your body reduces your core temperature and you don't want to be catching a cold at high altitude if you can help it.
Another alternative is that sometimes there are places that don’t necessarily have hot showers but you can get boiled water off heat from a stove. You can use it to wash when used with a big bucket and a small cup where you can throw it over yourself and have a good freshen up.