ハッブル宇宙望遠鏡の画像（銀河など）を、会社のホームページのデザインの一部として使うことは出来るのでしょうか？

This site also contains material generated, authored and/or prepared by individuals or institutions other than STScI, and those individuals or institutions may claim copyright. Should you desire use of such material at this time, inquiries should be made to those individuals and institutions in accordance with the following:

STScIに著作権が所属しないマテリアルも含まれていて、そのマテリアルの場合は著作権者に問い合わせる必要があります。

A catalogue of HST publicly released images on this site may be found at the following location: http://hubblesite.org/newscenter/. If the credit line for an image lists STScI as the source, the image may be freely used as in the public domain as noted above. However, for credit lines listing individuals from other institutions, you will need to contact that institution listed in the credit line to advise you on the copyright policy for that image. If the individual listed in the credit line is a member of the American Astronomical Society you can obtain their contact information from (https://members.aas.org/directory/directory.cfm).

ここでもSTScI以外の著作権者のマテリアルについて問い合わせるように求められています。

前後しますが、

Material credited to STScI on this site was created, authored, and/or prepared for NASA under Contract NAS5-26555. Unless otherwise specifically stated, no claim to copyright is being asserted by STScI and it may be freely used as in the public domain in accordance with NASA's contract. However, it is requested that in any subsequent use of this work NASA and STScI be given appropriate acknowledgement. STScI further requests voluntary reporting of all use, derivative creation, and other alteration of this work. Such reporting should be sent to copyright@stsci.edu.

強制的ではない（ボランタリ）が使用した旨の通知(acknowledgement)を求めてますね。

以上の点に留意すれば派生物(derivative creation)についても使用は可能です。

改変や商用として利用しない限り問題無いようです。

商用といっても画像を販売するなどのことで、HPデザインでの利用は大丈夫です。

できます。単なる自然物の撮影で著作権は発生しません。