You might know that all matter is made up out of atoms. Now, atoms themselves have a core, or nucleus, and electrons orbiting around the nucleus. The core has positive charge, the electrons have negative charge.
When you are rubbing the glass rod with the silk cloth, electrons are stripped away from the atoms in the glass and transferred to the silk cloth. This leaves the glass rod with more positive than negative charge, so you get a net positive charge.
Why do the electrons go from glass to silk and not from silk to glass? That depends a lot on the minute details of the material. Ultimately, for every two materials there is one of them where electrons are happier. It just turns out that for glass and silk, electrons are happier at the silk cloth.
Now to your second question. Here, the important thing to note is that in your typical solid material, the positive charges, which are the cores of the atoms, cannot move around much. They are locked into a rigid structure. The tiny electrons, however, can move around much better. That's why the glass rod can induce a net negative charge at one end of the paper clips.
EDIT: Let me add that there should also be some attraction between the silk and a bunch of paper: The electrons in the paper will be pushed away by the electrons in the silk, leaving the end of the paper that is closer to the silk with a net positive charge that then gets attracted. However, it might very well be that in your silk cloth the electrons are overall too spread out to have a strong enough attractive effect.
Charges can be added or removed to or from the surface of an insulator. This is what the experiment shows. Insulators only inhibit the flow of charges in its volume or along its surface. Such an addition or removal of charge to or from the surface of an insulator is, e.g., used in electrostatic generators like the van de Graaff generator.
Best Answer
Water is a polar molecule. It has a boomerang shape, with oxygen in the middle, which has a negative charge, and hydrogens at each end, which are positive. The hydrogens are sharing their electrons with the oxygen, but the oxygen is a bit "greedy", so it holds the electrons a bit tighter than the hydrogens do.
When you subject a thin steady stream of water to an electric charge, of either polarity, the water molecules tend to rotate so that their charges are aligned with the external charge, with opposite charges attracting and like charges repelling. So if you bring a positively charged rod near the stream, the negative sides of the water molecules turn towards the rod, and that attracts the stream towards the rod. And conversely, if you bring a negatively charged rod near the stream, the positive sides of the water molecules turn towards the rod, and that also attracts the stream towards the rod.
In contrast, oil molecules are non-polar. They are chains of say 15 to 50 carbon atoms, with hydrogens attached to every carbon. (There may also be a bit of branching in the carbon chain). The hydrogens are on the outside of the chain, so the positive charges of the hydrogen shield the negative charges of the carbons from the outside world. So if you bring a positively charged rod near an oil stream, the stream will be repelled, but it will be attracted by a negatively charged rod.
There are also some differences in behaviour because oil is not electrically conductive, but water is. (Actually, pure water isn't a great conductor, but even small amounts of dissolved salts & minerals increase its conductivity quite a bit).