According to the Edinburgh Journal of Science he borrowed the equipment installed at the Cape of Good Hope by the late Sir John Herschel and Dr Andrew Grant.
Grant and Herschel transported a massive set of lenses to the Cape in the mid 1830s. To give you an idea of the size of the thing, consider this passage from The New York Sun, dated August 25, 1835
Sir John Herschel had submitted his plans and calculations in adaptation to an object-glass of twenty-four feet in diameter: just six times the size of his venerable father's. For casting this ponderous mass, he selected the large glass-house of Messrs. Hartly and Grant, (the brother of our invaluable friend Dr. Grant) at Dumbarton. The material chosen was an amalgamation of two parts of the best crown with one of flint glass, the use of which, in separate lenses, constituted the great achromatic discovery of Dolland. It had been found, however, by accurate experiments, that the amalgam would as completely triumph over every impediment, both from refrangibility and discoloration, as the separate lenses. Five furnaces of the metal, carefully collected from productions of the manufactory, in both the kinds of glass, and known to be respectively of nearly perfect homogenous quality, were united, by one grand conductor, to the mould; and on the third of January, 1833, the first cast was effected. After cooling eight days, the mould was opened,a nd the glass found to be greatly flawed within eighteen inches of the centre. Nothwithstanding this failure, a new glass was more carefully cast on the 27th of the same month, which upon being opened during the first week of February, was found to be immaculately perfect, with the exception of two slight flaws so near the line of its circumference that they would be covered by the copper ring in which it was designed to be enclosed.
The weight of this ponderous lens was 14,826 lbs. or nearly seven tons after being polished; and its estimated magnifying power 42,000 times. It was therefore presumed ot be capable of representing objects in our lunar satellite of little more than eighteen inches in diameter, providing its focal image of them could be rendered distinct by the transfusion of article light. It was not, however, upon the mere illuminating power of the hydro-oxygen microscope, as applied to the focal pictures of this lens, that the younger Herschel depended for the realization of his ambitious theories and hopes. He calculated largely upon the almost unlimited applicability of this instrument as a second magnifier, which would supersede the use, and infinitely transcend the powers of the highest magnifiers in reflecting telescopes.
Now Lucas improved upon the Herschel design in several ways. First, he utilized a broader portion of the spectrum. Herschel made his lunar observations with the aforementioned gear in the mid 1830s but the Xray was not discovered until somewhat later in the century - 1895 by Wilhelm Roentgen - and the means of diffracting it were developed as part of the US hydrogen bomb project in the 1950s and 1960s. As a result, meaningful civilian application of Xray astronomy was not available until the early 1970s.
Lucas incorporated some of this technology into the Herschel telescope, enabling him to get better and more accurate images of the goings in in the Andromeda Galaxy, our closest Galactic neighbor. Still, Andromeda is more than 2,000,000 light years away which means that looking at it is like looking 2,000,000 years into the past. Even if the Millenium Falcon could manage the Kessel Run in 12 Parsecs, that still leaves more than 1,000 years at full speed and it's doubtful the hyperdrive would hold out that long.
This fan theory actually exists already. Lucas didn't witness these things happening but in fact came into possession of the Journal Of The Whills..
ET on the other hand, was based on documentary evidence that was shared with Lucas by the government as a diversionary tactic, despite him having read about the species as part of the galactic senate. This was how ET was able to recognise the trick or treater in the Yoda mask, as he was familiar with the species.
While the provenience of the telescope remains somewhat of a mystery, the second part of the question has a simple answer. When we on Earth see faraway objects in space, such as galaxies, we are necessarily observing their past, since light from those objects had to travel at finite speeds across space to reach us.
Although, personally, I suspect he took out substantial loans to pay for the telescope, only paying them off after the unprecedented commercial success of Howard the Duck.
Come on that's an easy one. The light from things far far away shows us things that happened a long time ago. Looking through telescopes does this all the time. And renting viewing time at some of the world's largest telescopes is expensive but not uncommon.