Terumot & Ma’aserot

I picked oranges from my tree, placed them in a bag, brought them inside and put them on the counter. I emptied the bag (or so I thought!) onto the counter, cut off more than 1%, and proceeded with the berachot and saying the text of separating terumot and ma'aserot.

A few minutes later, I realized that two oranges were still in the bag! I wasn't sure if I need to do the whole process again, since I did intend that the separation was for everything I picked. Granted, the oranges were still in the bag, but the bag was open and it was right next to the other oranges. Later on, I discovered that I had put an orange in my jacket pocket (and it was there with me at the time I separated terumot and ma'aserot.

What I did do was separate a bit from the two oranges (this was before I discovered the third in my pocket), and said the berachah without Hashem's name. Then I realized that it's best to just ask Torah VeHa'aretz Institute. J What do I do now, and does my second separation count?

I have a small vegetable patch in my yard. What is the order of the berachot on separating terumot and ma'aserot this year (5785)? Are we supposed to say the first berachah on separating terumot and maaserot and say the text? For the second berachah, are we supposed to substitute "ma'aser ani" for "ma'aser sheni"? Do we need to redeem it onto a coin? What do I do with the part of the vegetable I separated?

What amount of hefker (ownerless) fruit is obligated in teurmot and ma'aserot miderabanan? If produce in a private garden is declared ownerless, does it have hefker status?

Do we need to separate terumot and ma'aserot from produce found in closed military zones during the War of Iron Sword?

We picked lemons from our neighbor's tree with their permission. Some of the lemons were taken from the neighbors' garden and entered our house through the door. Another part was brought directly from their garden to our house through the window. The lemons are mixed together, so it is impossible to know which lemon was brought in through the door, and are obligated in tithes, and which lemons were brought in through the window and are not obligated. How should we separate terumot and ma'aserot now: Should we tithe each and every fruit, or can we take them all out of the house and bring them back in through the door?

There are people who prepare liqueur from the small fruits that grow on myrtle bushes (hadas) during this season of the year (hereinafter: "myrtle berries"). Is it necessary to separate terumot and ma'aserot from them?

My neighbor has a tree whose branches extend into my property. Am I allowed to pick the fruit without requesting permission?

I recently bought a hydroponics kit for my porch. Do fruits/vegetables that grow have the same halachot for shemitah, terumot, ma'aserot, neta revay, orlah? Also, which berachot would be said? Still ha’eitz or ha’adamah or shehakol?

I picked about 10 avocados last week and brought them home. Do I have to wait till they are soft and tasty to separate terumot and ma'aserot? I think you can eat them unripe though they are not tasty. 
But if I cut an unripe one for terumot and ma'aserot, I will have to throw away part since once cut,  avocados no longer ripen.
Also what do they do in supermarkets where terumot and ma'aserot have been taken but the avocados still need a week or 2 before they ripen and can be eaten?

Is it true that there is an arrangement where I pay money and terumot and ma’aserot are taken on my behalf?