Hi,
In opening I would like to say that I have a lot of love and respect for my Buddhist Brothers and Sisters, am a long-time Meditator of the breathe (8 years), and also study the Theravada school of thought.
<<1. Buddhism and Sikhism I think are largely similar, but they have a major difference that I find hard to reconcile. Buddhism (at least Theravadan and Zen) teaches that the existence of God can't be answered for sure.>>
I would tend to be in agreement with yourself with respect to Sikhi and Buddhism being similar.
My stance is that the Teachings that came through the Buddha are also found in the Guru Granth Sahib.
The difference with regards to God and no-God is, at one level, but a semantic one.
From my understanding Sikhs and Buddhists are both describing that Divinity is everywhere, and whilst Sikhs openly acknowledge it and perfectly comfortable with calling it God, Buddhists are, respectfully, indifferent to it.
For illustration purposes, imagine a pool of water from which all of life and everything has appeared from. Sikhs would see that as Divine and call it God; Buddhists would say that that was merely performing its natural function.
A further illustration, imagine someone you love, respect and admire. Sikhs would acknowledge that, Buddhists would see it too but say that it is just a person.
Both acknowledge it and recognise the attributes but have different stances, but that is all they are at the end, simply stances.
On a more practical level, I must admit that personally, the differences do begin to take effect over time. If I look at the person who I love in an indifferent way, which is not wholly incorrect when looked at from this perspective, one can see the cumulative effect.
As a Sikh I naturally and rightly believe that that God is everywhere and there is a feeling of love, comfort, warmth, a strong sense of security as well as belonging that comes with it.
When one is indifferent to it, it initially feels less then respectful to begin with, and then somewhat empty, and ultimately isolated as one progresses on the path.
Having gone through this, I have now reached a happy medium where fully acknowledge God is everywhere and meditate, do Prayer & Ardas, and Sewa too.
In Summary, Sikhi, at its most fundamental level recognizes, re-establishes, and fully acknowledges the most important relationship in life, which is with the Creator, Buddhist also see it, but are indiffent to the Creator.
<<and the same can be said for the soul.>>
Personally I believe in soul as The Guru and previous Teachers taught and it intuitively makes sense to me.
When on dies the spark of energy with you is extinguished and passes on in another Form, Rebirth as the Buddhists call it. That was the cause of you to be alive. There is a lot of debate about this even within Buddhism. Please look into Tathāgatagarbha - essentially that we already possess a seed, which when surrounded by the right conditions will flourish and allow us to become enlightened.
Note how this not that different to what the Guru has taught except that Sikhs acknowledge that the seed is Divine in origin.
<<Instead the Buddha says that we should forget such questions, and instead focus on achieving Nirvana, as these questions impede our spiritual growth. Sikhi (as far as I am aware) states that our ultimate purpose is to merge with God, and reach Sach Khand.>>
For Me, Sach Khand and Nirvana are essentially the same, once again semantics.
"Sach Khand: The Realm Of Formless Truth
...After experiencing the fourth realm, he becomes Self-realized. Once a devotee attains Self-realization, he becomes situated in this final realm of Truth, the ultimate stage of Spiritual experience of linking with the Absolute. ... It's also called in the Gurbani Chauthaa Pada (Fourth State) because it is beyond three qualities of Maya.... Param Anand (Bliss), Jeevanmukti (living liberated)... state of absolute Peace and tranquility, and so on. It is a state of existence in which the Aatmaan of the individual is linked and absorbed in the Mool, like a drop of water in the ocean.
...
At this point, the seeker has become one with his Mool (Source, Origin, Joti-Svaroopa...) within. Here, he identifies himself with the One True, Formless, Infinite Consciousness. Linked with his Origin, the Absolute Reality, his Soul links with the Spirit just as rivers merge with the ocean. This is the journey of an Spiritual aspirant. This journey begins from a material plane and ends at the Spiritual Plane. But, the SGGS asserts that those who have completed this journey are very "rare" in this world.
Source:
http://www.gurbani.org/articles/webart11.htm
<<The problem is, I can see and understand the reasoning behind both of these positions, and I have a really hard time figuring out what to believe on this issue. How can I resolve this conflict?>>
Ultimately practice is what matters.
Sikhs, such as myself sincerely have a lot of love, respect and reverence for the Buddha and his teachings but ultimately place thier faith the Guru, Dharma and Sangat as His teachings were complete, recorded and finalized through The Guru.
The Guru Granth Sahib has plurality at its heart and recognises that the teachings have been re-transmitted through a Noble Lineage which included Ram, Krishna and The Buddha, but recoginise that Enlightment will come through Nanak.
Ākẖahi keṯe kīṯe buḏẖ.
The many created Buddhas speak
Sri Guru Granth Sahib Ang 6
Nānak kahai kahāvai so▫e. ||5||12||
Says Nanak, I speak as He causes me to speak. ||5||12||
Thanks and hope that helps,
Lotus