התגובה שלו הייתה שקטה, אבל הייתה לי תחושה שהוא מסכים.

Because the nouns it refers to are feminine singular:

• תגובה = response/reaction, feminine
• תחושה = feeling/sense, feminine

In the past tense, היה / הייתה agrees with the noun it goes with.

So:

• התגובה שלו הייתה שקטה = His response was quiet
• הייתה לי תחושה = literally There was to me a feeling, meaning I had a feeling

Both תגובה and תחושה are feminine, so הייתה is the correct form both times.

The two instances do different jobs:

1. התגובה שלו הייתה שקטה
   Here הייתה is the ordinary past form of to be:
   His response was quiet.

2. אבל הייתה לי תחושה
   Here Hebrew uses a possession/existence pattern:
   היה/הייתה ל־... = someone had... / there was ... to someone

So הייתה לי תחושה literally means There was a feeling to me, but in natural English it means I had a feeling.

Hebrew often expresses possession with יש ל־... in the present and היה ל־... in the past.

Examples:

• יש לי ספר = I have a book
• היה לי זמן = I had time
• הייתה לי תחושה = I had a feeling

So instead of using a verb exactly like English to have, Hebrew often says something more like there was X to me.

Both are possible, but הייתה לי תחושה is a very common neutral order.

• הייתה לי תחושה = neutral, standard
• לי הייתה תחושה = puts more emphasis on לי (I had a feeling)

So the sentence as written sounds natural and unmarked.

Hebrew often expresses possession with:

• a noun + של
  • pronoun

So:

• התגובה שלו = his response
• literally: the response of him

There is also a more compact form:

• תגובתו = his response

But התגובה שלו is very common and feels natural in everyday Hebrew.
תגובתו is more formal or literary.

Because adjectives in Hebrew agree with the nouns they describe in gender and number.

Here:

• תגובה is feminine singular
• so the adjective must also be feminine singular: שקטה

Compare:

• תגובה שקטה = a quiet response
• תגובה שקטה הייתה לו = he had a quiet response
• התגובה שלו הייתה שקטה = his response was quiet

If the noun were masculine singular, you would use שקט.

Good question. שקטה literally means quiet, but in this sentence it describes the nature of the response, not just volume.

It can suggest things like:

• restrained
• subdued
• low-key
• not emotionally expressive
• not openly stated

So התגובה שלו הייתה שקטה can mean that his response was minimal, calm, or understated.

Depending on context, a speaker might also choose words like:

• מאופקת = restrained
• רגועה = calm
• מינימלית = minimal

But שקטה is understandable and natural enough.

The ש־ means that.

So:

• תחושה שהוא מסכים = a feeling that he agrees

In this sentence:

• הייתה לי תחושה שהוא מסכים = I had a feeling that he agrees / agreed

Hebrew uses ש־ to introduce many subordinate clauses, just like English uses that.

This is a very common point of confusion for English speakers.

In Hebrew, after a past expression like הייתה לי תחושה, the following verb may stay in the present if it describes a state or situation that was true at that time.

So:

• הייתה לי תחושה שהוא מסכים
  = I had the feeling that he agreed / was in agreement

Here מסכים describes a state: he is in agreement.

If you said:

• הייתה לי תחושה שהוא הסכים

that would sound more like I had the feeling that he had agreed or that he agreed at some specific point/event.

So מסכים is natural because it describes his ongoing stance, not a one-time completed action.

Because הוא is masculine singular, and the participle/present-tense form agrees with it.

• הוא מסכים = he agrees
• היא מסכימה = she agrees

So in שהוא מסכים, the masculine form is required because the subject is הוא.

In Hebrew, just like in English, agree can appear without an explicit object if the context makes it clear.

So:

• הוא מסכים = he agrees
• הוא מסכים איתי = he agrees with me
• הוא מסכים עם זה = he agrees with that

In your sentence, the speaker is just expressing a general sense that he was in agreement, so nothing more needs to be added.

Yes. אבל is the ordinary everyday word for but.

So:

• התגובה שלו הייתה שקטה, אבל הייתה לי תחושה שהוא מסכים.

sounds completely normal.

More formal alternatives exist, such as:

• אך
• אולם

But אבל is the most natural conversational choice.

Yes, it is natural and understandable.

A native speaker would understand it as something like:

• his response was quiet/subdued,
• but I had the feeling he agreed.

The one word some learners might pause over is שקטה, because English does not always describe a response as quiet in quite the same way. But in Hebrew it works, especially if the idea is that his reaction was restrained or not openly expressed.

So overall, the sentence is perfectly good Hebrew.