Great question.

A comprehensive answer would be a long one but here's a few thoughts.

Classical Christianity is, or may be interpreted to be, consistent with the Perennial view of God, so for research into this issue you have a wide range of literature to examine. Christianity was incomprehensible to me until I had studied Buddhism. This led me to the Classical teachings and the doctrine Divine Simplicity - which are carefully not taught by the modern Church.

I find it difficult to imagine what it would mean to say God has a personality or is a person, and feel it is a mere anthropomorphism.

But, many classical theists who accept divine simplicity and reject that God is a person are Christians, Muslims, and Jews. They do believe that God loves us, takes an interest in our life, is something we should worship, that there is an afterlife, etc. I don't understand how all these other beliefs follow (or even could follow, given that God is not a person).

These question can be answered but not briefly or quickly. This is an area of study and it is not conquered easily.

Plotinus warns us that when reading the sayings of the sages it is a good idea to put the phrase 'It is as if' in front of their words. They are describing the indescribable, and any words are bound to be capable of misleading. As Lao Tsu notes, the eternal Tao cannot be spoken and for his view the ultimate truth would be beyond conceptual fabrication.

When a person says God loves us he may have some idea of an old man with a beard, but he may also be dumbing down the idea that God is love. Not a personality that loves, but love as a fundamental phenomenon. This is connected with the notion that Reality is a Unity or 'non-dual'.

For a 'non-dual' explanation of God some texts that come to mind are: Being, Consciousness, Bliss by David Bentley Hart; God: A Guide for the Perplexed by Keith Ward: A Course in Miracles by Helen Schucman/Jesus. The latter is the one most likely to address your questions in detail, but it's a monster and is post-grad level in respect of religion and psychology. For the relationship beteeen God and Love there are also the books of Paul Ferrini. I would also recommend Plotinus and the poet Rumi. Someone who speaks clearly on God is Sadhguru and his talks can be found on youtube.

How do classical theists overcome the objection that their God is too impersonal to be of any significance to humans?

Obviously they are convinced in their own mind, which suggest there is no problem with the idea. The point to remember that for the Classical Christian any concept of God is false since He cannot be conceptualised. 'God' would be the ultimate nature of Reality and as such immediately accessible to all of us, but language could never capture His nature.

I feel it would be best to remain agnostic on the the question you've asked and spending a year or two browsing the 'Wisdom' literature. Good luck. I wish I could have answered the question directly but it would take a long time and much work and the authors I've mentioned and others do it much better and with more authority.

In fact the Classical view makes God even more loving than the Romanised teachings. It is a doctrine not just of forgiveness but of sinlessness. There would be no such thing as sin and nobody would condemned to eternal damnation. Love would be a basic property of Reality and a path to its hidden secrets.

EDIT: Answer 2. If you are seriously interested in this question then here's an idea. Get hold of a copy of The Perfume of Silence by Francis Lucille (the teacher of Rupert Spira) and read it while keeping in mind that when he speaks of Consciousness in its fundamental state he is speaking of what a Classical theist would call 'God'. Creation and evolution would take place in consciousness, not prior to it, and 'God' would be nothing like the deity of naive theism. This would be why the later Roman church crushed the gnostic form of Christian teachings and practice, burnt the books and knocked down the churches. Fortunately we now have the Nag Hammadi Library and can study what the original followers of Jesus had to say.