Can I apply "encrypt with public key and decrypt with private key concept" using ECC certificate?
You are right that (EC)IES essentially consists of a Diffie-Hellman key agreement and authenticated symmetric encryption, but the protocol flow is different. In particular, IES is a "one-shot" public-key encryption scheme: Assuming that Alice knows Bob's public key beforehand, she can encrypt a message for Bob "offline" without any interaction, just like with RSA.

In summary, ECIES consists of the following steps:


Assume Alice knows Bob's public key $Y=[y]P$.
Alice generates a random private key $x$ and computes $[x]Y$.
She derives a symmetric key $k$ from $[x]Y$.
Using some authenticated symmetric encryption algorithm, she encrypts her message using $k$ as the key, yielding a ciphertext $c$.
She transmits the pair $([x]P,c)$ to Bob.


Based on this, we can answer your questions:

1.
No, in IES the receiver (Bob) does not need Alice's long-term public key because she generates a fresh ephemeral key pair (whose public part is transmitted as part of the ciphertext) for each message. In fact, Alice does not even need to have a long-term key to be able to encrypt messages for Bob! This is in line with the general public key encryption setting: Everybody can encrypt, only Bob can decrypt.

2.: Yes, the encryption procedure for RSA is different from IES. But the protocol flow is not! Both are public-key encryption schemes.

3. No, according to 1.