I am Christadelphian and don't have a particular problem with the apostle's creed. It doesn't mention or imply the trinity... that was added later in church doctrine in our opinion. If the church believed in the trinity at that time, then surely it would have been explicit in the creed?
The accepted answer is wrong. It argues that because we don't agree with the current Catholic Church interpretation we can't agree with it. Yet just taking the original words (via translation) I can agree fully with the creed as written.
In the second part of your question, you ask how we have to interpret to agree with the creed. I've expanded on the creed (as translated to English in the link you posted) with inline comments to explain our beliefs and to show that they are consistent with the actual text of the creed.
I believe in God, the Father almighty,
creator of heaven and earth.
Here we understand God to be Yahweh, the creator of the heavens and the earth. The Father of Jesus.
I believe in Jesus Christ, his only Son, our Lord.
Jesus is the son of God, and our lord... not "God the son".
He was conceived by the power of the Holy Spirit and born of the virgin Mary.
Jesus was born human, with a human mother. Conceived by God, through His power, the holy spirit. The holy spirit is not a person, merely the power of God.
Jesus didn't receive the holy spirit until his baptism at 30 years old.
He suffered under Pontius Pilate,
was crucified, died, and was buried.
This is just a record of fact, established clearly from within scripture... and many historic records outside the scriptures.
He descended to the dead.
Assuming this is not talking of an underworld of any kind i.e. "hell". But merely saying he was in the ground, where all the dead are. In fact, it's interesting that this creed seems to support Christadelphian doctrine better than modern Christian doctrine in that it suggests all the dead descend... it doesn't say some ascend (heaven) and some descend (hell). Also of all people, the one person who "did no sin" would surely be ascending if there was a choice of merit.
Anyway, taking this as being in the tomb in the ground for 3 days, where the dead go. Then this is fine.
On the third day he rose again.
The foundation of the gospel - good message. Through Christ there is the hope of Resurrection, to be partakers of the promises to Abraham.
He ascended into heaven,
and is seated at the right hand of the Father.
Heaven is the dwelling place of God, and not somewhere where you go when you die. Christ ascending (to return in like manner as you saw him go up) is clear from scripture. He is at the right hand of his Father... he is not his own Father. With the whole world under his control - until he has put all his enemies under his feet, the last enemy being "death".
He will come again to judge the living and the dead.
He will return to this earth and raise the dead from the dust of the earth. Judging everyone and rewarding those who follow him in truth, by making them immortal "kings and priests" to be with him on this earth for 1000 years before giving back control of the earth to the creator... his Father.
I believe in the Holy Spirit,
We believe it exists and sustains all creation, the holy spirit gifts existed but are no longer in circulation as they have done their job of supporting and confirming the gospel message.
the Holy Catholic Church,
If this means the "original" first-century church - Ecclesia as we call it, based on the Greek. Then yes, we try and stick as close as possible to the original doctrines of the original (the meaning of the word Catholic, as I understand it) ecclesia (or church, is it's been translated in English).
We clearly don't agree with the doctrines of the current self termed "Catholic Church". Which in our opinion have gone on to add many other doctrines not held by the original Catholic church, or this creed.
the communion of the saints,
We call this the "breaking of bread" or "memorial meeting" held every Sunday.
the forgiveness of sins,
the resurrection of the body,
and the life everlasting. Amen.
I think all Christians can agree to this last part.
If you want more details of what Christadelphians believe, we have our own "creed" or what we call the statement of faith. It might be interesting for you to compare it to the "Apostles Creed" and see for yourself if it is consistent with it (the actual words, not the current interpretation of it). It highlights much of what I've said above, with a number of verses to back up each of the statements. It's freely available online, and I'd recommend it as a good source for our beliefs... It doesn't cover everything, but everyone who calls themselves Christadelphian must agree to these statements (either the original unamended version or the later amended version as the comment at the top of that page explains).
The Christadelphian Statement of Faith
Edit: I should point out that the above statement of faith was penned by Robert Roberts... so that covers the part of your question that asks about his beliefs.