wǒ yǐjīng yòng kǎhào jīhuó le xīn yínhángkǎ.

已经 is an adverb, and in Chinese adverbs usually come before the main verb phrase.

So in:

• 我已经用卡号激活了新银行卡。

the order is:

• 我 = subject
• 已经 = already
• 用卡号 = using the card number
• 激活了 = activated
• 新银行卡 = the new bank card

A rough pattern is:

• Subject + adverb + method/instrument + verb + object

So 已经 goes before the action as a whole, not after it.

Here 了 marks the action as completed.

• 激活 = to activate
• 激活了 = activated / have activated

So the sentence is talking about a finished action: the speaker has already completed the activation of the new bank card.

This 了 is the perfective aspect marker, not the sentence-final 了 that often shows a new situation.

Compare:

• 我激活新银行卡。 = I activate / I am activating the new bank card.
• 我激活了新银行卡。 = I activated / have activated the new bank card.

They are related, but they do different jobs.

• 已经 means already
• 了 marks the action as completed

Chinese often uses them together very naturally:

• 已经……了

This combination strongly suggests: the action has already been completed.

So:

• 我已经用卡号激活了新银行卡。

feels very natural for I have already activated the new bank card using the card number.

You can sometimes omit one of them, depending on context:

• 我已经用卡号激活新银行卡了。
• 我用卡号激活了新银行卡。

But 已经 + 了 is a very common and useful pattern.

用 means to use, and here it introduces the means or tool used to do something.

• 用卡号 = using the card number / with the card number

So the sentence is saying that the card number was the method used to activate the card.

Common pattern:

• 用 + tool/method + verb

Examples:

• 用手机付款 = pay with a phone
• 用微信登录 = log in with WeChat
• 用卡号激活 = activate using the card number

Chinese usually places things like method, tool, or manner before the verb.

English often says:

• activate the card with the card number

Chinese more naturally says:

• 用卡号 activate the card

So the Chinese order is:

• 我 已经 用卡号 激活了 新银行卡。

This is very common in Chinese:

• 用手机拍照 = take pictures with a phone
• 用钥匙开门 = open the door with a key

卡号 means card number.

It is a compact noun made of:

• 卡 = card
• 号 = number

In banking context, 卡号 normally means the number printed on the bank card.

Sometimes Chinese drops information that is obvious from context. Even though the full idea may be something like 银行卡号 (bank card number), just 卡号 is often enough if everyone already knows you are talking about a bank card.

Both can be correct, but 新银行卡 is very natural and concise.

In Chinese, when a simple adjective directly modifies a noun, 的 is often omitted, especially in set or common combinations.

So:

• 新银行卡 = new bank card
• 新的银行卡 = new bank card

The version without 的 often sounds tighter and more noun-like.

A useful rough rule:

• shorter, common, close adjective+noun combinations often omit 的
• adding 的 can sound a bit more descriptive or emphatic

In this sentence, 新银行卡 sounds very natural.

Because the sentence is not counting the card and does not use a demonstrative like 这 or 那.

Measure words are usually needed in patterns like:

• 一张银行卡 = one bank card
• 这张银行卡 = this bank card
• 那张银行卡 = that bank card

But when a noun appears by itself as the object, you do not need a measure word:

• 激活银行卡 = activate a bank card / bank cards
• 激活了新银行卡 = activated the new bank card

So no measure word is needed here.

Yes, it could.

For example:

• 我已经用卡号把新银行卡激活了。

This is also grammatical.

The 把 structure highlights what happened to the object:

• 把新银行卡激活了 = got the new bank card activated

But 把 is not required here. The original sentence is already completely natural:

• 我已经用卡号激活了新银行卡。

So the difference is mostly one of focus and style, not basic meaning.

Because the basic Chinese word order is:

• Subject + Verb + Object

So:

• 我 = subject
• 激活了 = verb
• 新银行卡 = object

The phrase 用卡号 is not the object. It is an instrument/method phrase, so it comes before the verb.

That gives:

• 我 已经 用卡号 激活了 新银行卡。

This is a very standard Chinese sentence pattern.

Both can appear in banking contexts, but they are not exactly the same.

激活

means activate

• make a card/account/device become usable

开通

often means open / enable / start a service

• open a bank account
• enable mobile banking
• activate a service feature

For a bank card, 激活 is very common when the card exists already but has not yet been made usable.

So:

• 激活银行卡 = activate a bank card

Depending on context, 开通 might be used for a service connected to the card, but 激活 is the clearest choice here.

Sometimes yes, if the subject is obvious from context.

For example, in a conversation:

• 已经用卡号激活了新银行卡。

could be understood as [I] already activated the new bank card using the card number.

However, when giving a full standalone sentence, keeping 我 is clearer and more standard:

• 我已经用卡号激活了新银行卡。

Chinese often drops subjects in context, but learners should include them unless the context clearly makes them unnecessary.

It functions as a single compound noun meaning bank card.

It is built from:

• 银行 = bank
• 卡 = card

So:

• 银行卡 = bank card

Chinese often forms nouns by combining smaller meaningful parts. This is extremely common and useful to notice when learning vocabulary.

Similarly:

• 卡号 = card number
• 银行卡号 = bank card number

A very useful pattern here is:

• Subject + 已经 + 用 + tool/method + verb + 了 + object

Using this pattern, you can make many similar sentences:

• 我已经用手机付了款。
  I have already paid with my phone.

• 他已经用密码登录了账户。
  He has already logged into the account using the password.

• 我们已经用邮件确认了信息。
  We have already confirmed the information by email.

So this sentence is a good model for talking about a completed action and the method used to do it.