Approximately with ころ and くらい, and limits with まで, ほど, すぎる

ころ is a noun that roughly means "approximate time". You run into Xのころに a lot. This can either be a conjunction "around the time of X", or a noun like "the general time when X" with the に particle attached. In some situations ころ can attach directly to nouns as the suffix ごろ.

子供のころに見たアニメを思い出す。
I remembered an anime I watched when I was a child.

そういえば、去年の今ごろだったかな？
Oh right, it was around this time last year I guess?

くらい takes a measure or amount (including time) and makes it approximate. It is completely interchangeable with ぐらい and it is entirely up to speaker’s preference.

午後1時ぐらいで大丈夫？
Is around 1pm okay?

It can also be used to mean “to the point where” or “to the level where” and not an inch beyond that.

毎日食べたいくらい美味しかったです
It was delicious to the point where I’d want to eat it every day.

When paired with the は particle it gives a nuance of “at least”.

名前くらいは聞いたことがあるだろう。
You must have at least heard of its name.

まで essentially means "up to" or "until". The limit or boundary marked by まで is included in the set.

世界が終わる日まで。
Until the day the world ends.

まで is often paired with から as 〜から〜まで (from 〜 until 〜).

小さなことから、大きなことまで。
From the small things to the big things.

までに changes the meaning of まで to mean “by” (as in “do something by next Friday”)

明後日までには終わらせます。
I will finish it by the day after tomorrow.

ほど essentially means "as" in terms of a comparison. Deep down the core meaning of ほど is “to the extent of”.

私は彼らほど強くない。
I am not as strong as them.

In positive statements where ほど attaches to an "amount", it's an approximation.

中身はまだ半分ほど残っている。
About half of the contents were still left.

すぎる is a verb and means "to exceed" or "to surpass". As an auxiliary verb, it means "too much" or indicates an excess of activity. It attaches to the ます stem.

美味しいものを食べすぎた。
I ate too much good stuff.