Learn Hardcore Russian: На этом шоу ведущая задаёт гостям смешные вопросы. - On this show the female host asks the guests funny questions.

case (nominative is typical for the subject; ведущая is nominative singular feminine)
agreement with the verb (ведущая is feminine singular; задаёт is 3rd person singular, which matches)

Why is it ведущая and not ведущий?

Both come from the same base:

ведущий – literally leading, but also host/presenter (usually masculine or generic)
ведущая – the feminine form, referring to a female host

The ending:

-ий / -ый → masculine (ведущий)
-ая → feminine (ведущая)

So ведущая is used because the host in this sentence is female.

Is ведущая an adjective or a noun here?

Historically it comes from a present active participle (the one who leads), but in modern usage here it functions as a noun:

ведущая = female host / presenter (profession/role)

You can tell it’s a noun in this context because:

it stands alone without another noun after it
it’s the subject of the verb задаёт

Why is it на этом шоу and not в этом шоу?

With events, activities, programs and similar, Russian very often uses на:

на концерте – at a concert
на уроке – in class
на экзамене – at the exam
на шоу – on/at the show

So на этом шоу is the natural idiomatic way to say on this show / on this program.
В этом шоу is not wrong grammatically, but it sounds less idiomatic and more like inside this show as a kind of “space,” which is not how Russians usually conceptualize TV/radio shows.

What case is этом шоу, and how do I know?

Этом шоу is in the prepositional case, used here with на to indicate place/situation: on this show.

You can see this from этом:

masculine/neuter prepositional singular of этот is этом (о ком? о чём? – об этом)
the noun шоу is indeclinable (it doesn’t change form in cases), so it stays шоу in all cases.

So:

на этом шоу = on this show (prepositional singular).

What is the infinitive of задаёт, and how is it conjugated?

The infinitive is задавать (imperfective).

Conjugation (present tense):

я задаю
ты задаёшь
он/она/оно задаёт
мы задаём
вы задаёте
они задают

In our sentence, задаёт is:

3rd person singular
present tense
imperfective aspect

It means she asks / is asking (regularly, generally, or right now depending on context).

What’s the difference between задавать вопросы and спрашивать?

Both involve asking, but there are typical patterns:

задавать (кому?) вопросы (о чём? / какие?)
- literally to pose questions
- emphasizes the act of putting formal or explicit questions
- often used in more “official” or structured contexts: interviews, TV shows, exams
- e.g. ведущая задаёт вопросы гостям – the host asks the guests questions
спрашивать (кого? о чём? / что?)
- to ask, to inquire
- more general, for everyday “to ask (someone)”
- e.g. я спрашиваю друга о фильме – I ask my friend about the film

In this context (a show host posing questions to guests), задавать вопросы is the more natural choice.

Why is гостям in the dative case and not гостей?

The verb задавать (вопросы) takes a dative person and an accusative thing:

задавать что? → вопросы (accusative plural)
кому? → гостям (dative plural)

So the pattern is:

задавать гостям вопросы = to ask guests questions
literally: to pose to-guests questions.

If you used гостей (accusative), it would suggest the guests are the direct object, which doesn’t match the government of задавать (вопросы). The guests here are the indirect object (the recipients of the questions), so they must be in the dative case.

What are the main forms of гость (guest), and how do we get гостям?

Гость is a masculine noun (ending in soft sign -ь). Key forms:

Singular:

Nominative: гость – guest
Genitive: гостя
Dative: гостю
Accusative: гостя
Instrumental: гостем
Prepositional: госте

Plural:

Nominative: гости – guests
Genitive: гостей
Dative: гостям – to the guests
Accusative: гостей
Instrumental: гостями
Prepositional: гостях

In our sentence, гостям = dative plural (to the guests), because the questions are addressed to them.

Why is it смешные вопросы, and what is happening grammatically?

Смешные вопросы consists of:

смешные – adjective, plural
вопросы – noun, plural

They agree in:

number: both plural
gender: вопросы is masculine plural; смешные is the generic plural form
case: accusative plural (direct object of задаёт)

For inanimate masculine nouns, accusative plural = nominative plural, so:

nominative plural: смешные вопросы
accusative plural: смешные вопросы (same form)

Meaning:

смешные = funny, sometimes also silly/amusing depending on context.

Can the word order be different, for example: Ведущая на этом шоу задаёт гостям смешные вопросы?

Yes. Russian word order is flexible. Some common variants:

На этом шоу ведущая задаёт гостям смешные вопросы.
- Focus on the setting first: On this show, the host…
Ведущая на этом шоу задаёт гостям смешные вопросы.
- Starts with the subject: The host on this show asks…
Ведущая задаёт гостям смешные вопросы на этом шоу.
- Puts the show information at the end, as an afterthought or emphasis.

All are grammatically correct. The chosen order in the original sentence emphasizes the show as the context right from the beginning.

Why do I sometimes see задаёт written as задает without ё?

In standard Russian spelling, ё is often replaced by е in non-ambiguous cases, especially in print:

задаёт → задает
всё → все (in many texts)
идёт → идет

Pronunciation, however, stays [ё], not [е].
So задаёт is pronounced [задaйот], even if written задает.

In learning materials and dictionaries, ё is usually kept to help with correct pronunciation.

What is the aspect of задаёт and how would the perfective change the meaning?

Задаёт comes from задавать – imperfective aspect.

Imperfective (задавать) is used for:

ongoing actions
repeated/habitual actions
processes in general

Here it suggests a typical or repeated behavior on the show: the host (usually/regularly) asks the guests funny questions.

The perfective counterpart is задать. Its 3rd person singular future is:

она задаст – she will ask (once / in a specific instance)

So:

Она задаёт гостям смешные вопросы. – She (generally/regularly) asks the guests funny questions.
Она задаст гостям смешные вопросы. – She will ask (at some point, in a concrete situation) funny questions to the guests.

Does Russian distinguish between “she asks” and “she is asking” like English does?

No. Russian has one present tense for both:

Она задаёт гостям смешные вопросы.

Depending on context, this can mean:

She asks the guests funny questions (habitually, in general)
She is asking the guests funny questions (right now)

The difference between simple and continuous present in English is usually conveyed in Russian by:

context
adverbs (e.g. сейчас – now, обычно – usually)
aspect sometimes, but in the present tense of imperfective it still covers both meanings.