Hi John! welcome to S&S ! I am so pleased to see a Hekate thread! I just love Her!
I hope you dont mind me hijacking your thread here, but I work quite closely with Hekate and thought i could offer my own perspective.
1)I think its normal for any deity to feel far or close at various times. They dont need to be up in our faces 24 hours a day 7 days a week. I think they come close to us when we need them most and call on them but when its time to stand on our own two feet and either use what they've taught us or experience something we need to, they will pull back a bit. Never to desert us, just to let us have our "human experience". Hekate is very powerful and obviously magickal and while she *could* in theory wave her hand and make us all knowing, all powerful, she wouldnt do that- she will guide you on your magickal path and help you along the way and sometimes that means her stepping back and letting you try something out for yourself. In short, yes what you are saying is perfectly normal with Her or any other deity
2) Yes, she will have heard all of your requests, dreams, desires, wants etc. but, just because She has HEARD them and is aware of them, it doesnt mean you will get them. Many times we DONT get things we so desperately want for various reasons. Sometimes it's because of blocks in ourselves that we need work on, sometimes that thing we want so badly just isnt in the cards for us at this point in time. Sometimes something even BETTER is right around the corner. They dont work for us, they work with us to achieve our goals. Sometimes we dont get it because we dont work hard enough for it or put enough effort in to achieving it. There are various reasons but thats the good thing about magick. It helps align the energies to your will. Hekate is a VERY good magick teacher. She will teach those who show initiative and desire. I have seen her manifest some things pretty darn quick in my own life.
3) She will see your efforts.

In my own personal experience with Her and my own walk with Hekate- shes very motherly and dark. For me, she lets me make my mistakes then will tell me where I've gone wrong. Offerings I've given her : honey, candles, frankincense, blood (during rituals) an altar with bones decorating it, magickal items ive made, herbal mixes... I believe deities appreciate all offerings given to them and the energy and intent behind the offerings. even if you dont have much and can only offer one thing- if your intent is genuine, the offering is ten times better than one or a dozen given out of greed.
4) I have seen her manifest things in an amazing way in my own life and those of others. While Her purpose is not that of a genie in a bottle to grant wishes and desires, those she finds favor with generally are able to manifest many desires through Her guidance and help.