"This is mom."
I don't know what sort of device you are on, but on a desktop you can use an extension called DuoKeyboard (unfortunately only on Chrome though) that shows the Cyrillic keymap for reference on the exercise screen and automatically switches your layout, so you can type Cyrillic handily. You can also use something like the branah.com virtual keyboard which additionally allows you to click on the letters you want, they will appear in a text box and you can copy-paste them from there to the exercise screen.
I don't use mobiles, but I'm under the impression that similarly to desktops, you can install multiple keymaps and switch between them with one tap. I've seen at least a Windows Phone do that.
On a mobile phone, you can use the Multiling Keyboard App which enables many languages, including Russian.
On a PC, you can enable a Russian keyboard as well - just the order of the letters is completely different from what you are used to (except for c, which is on the c). But if you're serious with learning Russian, you can look for a programme that will help you learn to type Russian. I used Stamina, which comes with funny error noises. I am very amazed how my brain can sort out the different keyboards. Only when typing other Slavic languages with Latin letters, my brain sometimes wants to switch to the Russian keyboard layout, and then it gets really interesting. :D
I typed 'Это ма́ма', and was told I had a TYPO becuase I had INCLUDED the accent on ма́ма. However, in the first question of this lesson (select the right word - with photos) it was spelt ма́ма. a) What is the correct spelling of ма́ма please? b) Is there some subtle difference that I am missing between 'ма́ма' and 'мама'? Thanks!
"Это мама" would be the ultimately correct spelling, since Russian does not actually use any graphic accents. However, for learning's sake, there are usually accents placed in order to know where the stress is. So, "мáма" is the correct form when using accents to indicate stress, but there is no difference between that and "мама", which is how a native Russian would write it.
"Эта мама" is a phrase "this mom", "это мама" is a sentence meaning "this is mom". You always use "это" in "this is..." sentences. The other forms such as "эта" are used only when the word is being used as an adjective. See olimo's guide for a more detailed explanation: https://www.duolingo.com/comment/11536858
I don't know if you're using the website, but on the web the course allows for transliteration. You can type in English letters.
For android devices trying to type in Cyrillic. Download the Microsoft swift keyboard and then add Russian to the languages in settings. You can then swipe the space key to change from English to Cyrillic keyboards easily. I'm unsure weather you can download the same on an ios device