Be, have, live
The ways to say something is there or that you have it — aru for things, iru for people and animals, motteru for what you own or carry — plus sumu for where you live.
aru
polite arimasuthere is; have (things)
ある あります
States that a thing, event or amount exists or is available, and is the default 'have' for time, plans and things (jikan aru?), with the thing marked by ga.
uchi ni kasa aru?
Do you have an umbrella at home?
うちに傘ある?
uchi ni kasa ga arimasu ka?
Do you have an umbrella at home?
うちに傘がありますか?
The negative is the separate word nai (kasa nai), never *aranai.
iru
polite imasube, exist; have (people, pets)
いる います
Says where a person or animal is or that they exist (ima doko ni iru?), is the 'have' for people and animals (kyoudai iru?, kanojo iru?, inu iru?), and is the base that -teru is built on.
ima uchi ni iru?
Are you home right now?
今うちにいる?
ima uchi ni imasu ka?
Are you home right now?
今うちにいますか?
Homophone iru 'need' (要る) is godan: iranai, itte.
motsu
polite mochimasuhold; carry; have
持つ もつ 持ちます
Holding or carrying something, and in the -teru form owning or having it on you (kuruma motteru?), with motte iku / motte kuru meaning take / bring.
ima kasa motteru?
Do you have an umbrella on you?
今傘持ってる?
ima kasa mottemasu ka?
Do you have an umbrella with you?
今傘持ってますか?
Owning or having it on you is motteru; bare motsu is 'hold / carry' (motou ka? = shall I carry that?) and also 'last' (ashita made motsu, karada ga motanai).
sumu
polite sumimasulive (in a place)
住む すむ 住みます
Says where someone lives, with the place marked by ni; your current home takes the -teru form (doko ni sunderu?), the plain form is for a move ahead (rainen toukyou ni sumu) and -tai for a wish (toukyou ni sumitai).
doko ni sunderu?
Where do you live?
どこに住んでる?
doko ni sundemasu ka?
Where do you live?
どこに住んでますか?
Homophone sumu 'be over, be settled' (済む) also gives sunde, sunda, and its polite negative is sumimasen (sorry), one sound off sumimasu; for where you live now say sundemasu, and 'I don't live there' is sundenai / sundemasen.
Learn first: -teru