It is important to make is the distinction between musical compositions and sound recordings. This means that even if an orchestra is performing a public domain work, that particular recording is protected by Copyright Law. And, permission to use a copyrighted composition does not give you any rights to use a sound recording. Definitions from Copyright.gov are as follows:
A Musical Composition consists of music, including any accompanying words, and is normally registered as a work of performing arts. The author of a musical composition is generally the composer and the lyricist, if any. A musical composition may be in the form of a notated copy (for example, sheet music) or in the form of a phonorecord (for example, cassette tape, LP, or CD).
A Sound Recording results from the fixation of a series of musical, spoken, or other sounds. The author of a sound recording is the performer(s) whose performance is fixed, or the record producer who processes the sounds and fixes them in the final recording, or both.
For published works, this copyright is typically held by the publishing company and not the composer. A composer distributing photocopied or PDF copies of their own pieces owned by the publishing company would be violating copyright law.
Performing Rights Organizations (PROs) such as ASCAP and BMI grant businesses and venues blanket rights that encompass all of the artists the organizations represent. Establishments that possess such a blanket license do not need to seek permission for each individual artist or song that they wish to play publicly; examples could include a restaurant that plays music throughout, or a bar that regularly hosts DJs and live bands.
The blanket licenses that PROs provide apply only to playing music. If you are interested in putting on a musical, opera, ballet, or other staged work that requires acting or choreography, these "small rights" granted by blanket licenses are inadequate. You will instead need to contact the publisher and ask about all-encompassing grand rights that are assessed on a case-by-case basis. Similarly, attempting to approximate a production of the musical Grease by piecing together arrangements could be a violation of copyright.
When a musical composition is in the public domain, you do not need to worry about securing rights to perform the work (e.g. play the work for a concert, upload a cover of the work to YouTube, etc.). You are also free to create derivative works, including arrangements, re-orchestrations or harmonizations, or adding/changing texts. If the work is not in the public domain, you must first secure rights to do any of the above unless your purpose could be ruled fair use.
It depends on the type of derivative work: certain elements of a publication may be protected by copyright while others may not. For example, Bärenreiter-Verlag's edition of the Mozart Requiem is technically protected by copyright, but the protection only applies to Heinz Moehn's piano reduction and Christoph Wolff's foreword (and its translation). The original content of the Requiem is still public domain; therefore, photocopying the orchestral score or instrumental parts would not constitute a violation of copyright. (The same could not be said of the vocal score, which bears the piano reduction, though you may still be able to claim fair use.)
Arrangements and transcriptions are fuzzier. Like with piano reductions, re-orchestrations, simplifications, and more elaborate arrangements are protected by copyright in their entirety if they are not already released to the public domain. For example, Barbara Buehlman's 1970 transcription Blessed Are They (based on the first movement of Brahms' Ein deutsches Requiem, "Selig sind, die da Leid tragen") is a protected work; not the motivic material, mind, but it would still very much be a violation of copyright law to photocopy either the score or individual parts. Since Buehlman died in 1997, the work will not release to the public domain until 2067.
The short answer is no. Prior to 1972, almost all recordings were protected by state law; current federal states that these recordings will remain protected by copyright until 2067. And since 1989, even unpublished recordings are protected by copyright law for the life of the author plus at least 70 years.