"Do you remember that person's face?"
When you ask someone if they 'remember' something, you are asking in the present tense. As Japanese combines the present and future tense this can be tricky. おぼえますか would be closer to 'will you remember' or 'will you memorize'. To emphasize 'in this moment'/'currently' it is necessary to use the て form.
For example: 「書いていますか」 'Are you writing?' vs. 「書きますか」 'Do you write?'.
The main issue would be that, in English, using the word 'remember' also involves a temporal article 'do you', 'will you', 'did you', etc. As this does not apply to Japanese the conjugation of 'remember' is more important.
Many people prefer to think of 覚える as 'memorize' (place in memory) or 'learn' and 覚えている as 'remember' (pull from memory).
Not necessarily, if you're pointing at a name on a piece of paper near the listener, then その人 would be a reasonable way to phrase it.
I realize that there is a massive call among the various discussions for the greater use of Kanji in both the questions and the answers. But am I the only one who finds it a cheat on Duo's part that they give the English sentence for us to translate, hiragana for the words to select from, but Kanji for the drop-down hints?
As your example shows, Duo wants かおをおぼえて, but the hints show only 顔を覚えて - which Duo will not accept (or at least does not have as an option)..
It would be even more amazing if the software would adapt to your knowledge of kanji. Like if you know lots of kanji already. But there's a million ways it feels like I'm ahead of my placement for japanese on DL. I wish the learning was more adaptive to what I know, but i realize that is easier said/requested than done.
It keeps saying 'jin' for 'hito' and it's a word that is more frequently used on DL as a standalone noun, thus 'hito', so I wish they'd change that audio. There are a couple words like that and I am concerned that some people could be learning that basic word wrong if they don't know better.